Value | Name | Graphics | Symbol | LaTeX | Formula | Nº | OEIS | Continued fraction | Year | Web format |
0.74048 04896 93061 04116[Mw 1] |
Hermite constant Sphere packing 3D Kepler conjecture[1] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Pyramid_of_35_spheres_animation_large.gif/100px-Pyramid_of_35_spheres_animation_large.gif) |
![{\displaystyle {\mu _{_{K}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/adaec6de807844bd701af9c8a3926d3f5ef92b61) |
The Flyspeck project, led by Thomas Hales, demonstrated in 2014 that Kepler's conjecture is true.[2] |
|
|
ਫਰਮਾ:OEIS2C |
[0;1,2,1,5,1,4,2,2,1,1,2,2,2,6,1,1,1,5,2,1,1,1, ...] |
1611 |
0.74048048969306104116931349834344894 |
22.45915 77183 61045 47342 |
pi^e[3] |
|
![{\displaystyle \pi ^{e}}](//wikimedia.org/api/rest_v1/media/math/render/svg/eb60fab89f41a1248e5d94a6f3d338b862c77a19) |
![{\displaystyle \pi ^{e}}](//wikimedia.org/api/rest_v1/media/math/render/svg/eb60fab89f41a1248e5d94a6f3d338b862c77a19) |
|
|
ਫਰਮਾ:OEIS2C |
[22;2,5,1,1,1,1,1,3,2,1,1,3,9,15,25,1,1,5,...] |
|
22.4591577183610454734271522045437350 |
2.80777 02420 28519 36522[Mw 2] |
Fransén-Robinson constant[4] |
|
![{\displaystyle {F}}](//wikimedia.org/api/rest_v1/media/math/render/svg/265b6cfb92e9e697cf7051b0e829d117748377cf) |
![{\displaystyle \int _{0}^{\infty }{\frac {1}{\Gamma (x)}}\,dx.=e+\int _{0}^{\infty }{\frac {e^{-x}}{\pi ^{2}+\ln ^{2}x}}\,dx}](//wikimedia.org/api/rest_v1/media/math/render/svg/d6e2cca8176503bda557cdaf124f090b7ac09ff3) |
N[int[0 to ∞] {1/Gamma(x)}]
|
|
ਫਰਮਾ:OEIS2C |
[2;1,4,4,1,18,5,1,3,4,1,5,3,6,1,1,1,5,1,1,1...] |
1978 |
2.80777024202851936522150118655777293 |
1.30568 6729 ≈ by Thomas & Dhar 1.30568 8 ≈ by McMullen[Mw 3] |
Fractal dimension of the Apollonian packing of circles [5] · [6] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/ApollonianGasket-15_32_32_33.svg/100px-ApollonianGasket-15_32_32_33.svg.png) |
![{\displaystyle \varepsilon }](//wikimedia.org/api/rest_v1/media/math/render/svg/a30c89172e5b88edbd45d3e2772c7f5e562e5173) |
|
|
|
ਫਰਮਾ:OEIS2C |
[0;3,2,3,16,8,10,3,1,1,2,1,3,1,2,13,1,1,4,1,5,...] |
1994 1998 |
1.305686729 ≈ 1.305688 ≈ |
0.43828 29367 27032 11162
0.36059 24718 71385 485 i[Mw 4] |
Infinite Tetration of i[7] |
|
![{\displaystyle {}^{\infty }{i}}](//wikimedia.org/api/rest_v1/media/math/render/svg/049ea9eeb550a19d05c5cb54b76b711bd487bebc) |
![{\displaystyle \lim _{n\to \infty }{}^{n}i=\lim _{n\to \infty }\underbrace {i^{i^{\cdot ^{\cdot ^{i}}}}} _{n}}](//wikimedia.org/api/rest_v1/media/math/render/svg/7397c0a37b5f711c84ea35561af1122876953692) |
|
C |
ਫਰਮਾ:OEIS2C ਫਰਮਾ:OEIS2C |
[0;2,3,1,1,4,2,2,1,10,2,1,3,1,8,2,1,2,1, ...] + [0;2,1,3,2,2,3,1,5,5,1,2,1,10,10,6,1,1...] i |
|
0.43828293672703211162697516355126482 + 0.36059247187138548595294052690600 i |
0.92883 58271[Mw 5] |
Sum of the reciprocals of the averages of the twin prime pairs, JJGJJG |
|
![{\displaystyle B_{1}}](//wikimedia.org/api/rest_v1/media/math/render/svg/1fa091eb428443c9c5c5fcf32a69d3665c89e00c) |
![{\displaystyle {\frac {1}{4}}+{\frac {1}{6}}+{\frac {1}{12}}+{\frac {1}{18}}+{\frac {1}{30}}+{\frac {1}{42}}+{\frac {1}{60}}+{\frac {1}{72}}+\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/7fbc5e3b168d1de72c891169b96b96c24afb908d) |
1/4 + 1/6 + 1/12 + 1/18 + 1/30 + 1/42 + 1/60 + 1/72 + ...
|
|
ਫਰਮਾ:OEIS2C |
[0; 1, 13, 19, 4, 2, 3, 1, 1] |
2014 |
0.928835827131 |
0.63092 97535 71457 43709[Mw 6] |
Fractal dimension of the Cantor set[8] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Cantor5.svg/100px-Cantor5.svg.png) |
![{\displaystyle d_{f}(k)}](//wikimedia.org/api/rest_v1/media/math/render/svg/33ea7d98d0687ec762539d71e5aa71bf10eb3d99) |
![{\displaystyle \lim _{\varepsilon \to 0}{\frac {\log N(\varepsilon )}{\log(1/\varepsilon )}}={\frac {\log 2}{\log 3}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/76743e783bd226619361220b74621e1e87aca8a0) |
|
T |
ਫਰਮਾ:OEIS2C |
[0;1,1,1,2,2,3,1,5,2,23,2,2,1,1,55,1,4,3,1,1,...] |
|
0.63092975357145743709952711434276085 |
0.31830 98861 83790 67153[Mw 7] |
।nverse of Pi, Ramanujan[9] |
|
![{\displaystyle {\frac {1}{\pi }}}](//wikimedia.org/api/rest_v1/media/math/render/svg/c6b81c585f1905cd13e59550b847006593be2e13) |
![{\displaystyle {\frac {2{\sqrt {2}}}{9801}}\sum _{n=0}^{\infty }{\frac {(4n)!\,(1103+26390\;n)}{(n!)^{4}\,396^{4n}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/d1a95c38a8e6823a02cbb7160d58715d7770470c) |
2 sqrt(2)/9801
* Sum[n=0 to ∞]
{((4n)!/n!^4)
*(1103+ 26390n)
/ 396^(4n)}
|
T |
ਫਰਮਾ:OEIS2C |
[0;3,7,15,292,1,1,1,2,1,3,1,14,2,1,1,2,2,2,...] |
|
0.31830988618379067153776752674502872 |
0.28878 80950 86602 42127[Mw 8] |
Flajolet and Richmond[10] |
|
![{\displaystyle {Q}}](//wikimedia.org/api/rest_v1/media/math/render/svg/6d07aa40096410d8a45588baa42452ae706d0156) |
![{\displaystyle \prod _{n=1}^{\infty }\left(1-{\frac {1}{2^{n}}}\right)=\left(1{-}{\frac {1}{2^{1}}}\right)\left(1{-}{\frac {1}{2^{2}}}\right)\left(1{-}{\frac {1}{2^{3}}}\right)...}](//wikimedia.org/api/rest_v1/media/math/render/svg/20002f989c68ad24b8c74ff9e02b20b0e985958d) |
|
|
ਫਰਮਾ:OEIS2C |
[0;3,2,6,4,1,2,1,9,2,1,2,3,2,3,5,1,2,1,1,6,1,...] |
1992 |
0.28878809508660242127889972192923078 |
1.53960 07178 39002 03869[Mw 9] |
Lieb's square ice constant[11] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/a/a8/Sixvertex2.png/100px-Sixvertex2.png) |
![{\displaystyle {W}_{2D}}](//wikimedia.org/api/rest_v1/media/math/render/svg/e50afbb73e4ab150652ec695c9cb9e2b1c48a4d1) |
![{\displaystyle \lim _{n\to \infty }(f(n))^{n^{-2}}=\left({\frac {4}{3}}\right)^{\frac {3}{2}}={\frac {8}{3{\sqrt {3}}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/27f7257c3ade85cf68f16f38b871c68d95dec8d9) |
|
A |
ਫਰਮਾ:OEIS2C |
[1;1,1,5,1,4,2,1,6,1,6,1,2,4,1,5,1,1,2,...] |
1967 |
1.53960071783900203869106341467188655 |
0.20787 95763 50761 90854[Mw 10] |
[12] |
|
![{\displaystyle i^{i}}](//wikimedia.org/api/rest_v1/media/math/render/svg/7d4035ae18d005ce695d4fc30cb23c0771ab4cd8) |
![{\displaystyle e^{-{\frac {\pi }{2}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/83b4f076844ded4ce5d6d8f14b954f20bf18468c) |
|
T |
ਫਰਮਾ:OEIS2C |
[0;4,1,4,3,1,1,1,1,1,1,1,1,7,1,20,1,3,6,10,...] |
1746 |
0.20787957635076190854695561983497877 |
4.53236 01418 27193 80962 |
Van der Pauw constant |
|
![{\displaystyle {\alpha }}](//wikimedia.org/api/rest_v1/media/math/render/svg/6289622b3b197c568f6e73e678814e9cb4c8a81b) |
![{\displaystyle {\frac {\pi }{\ln(2)}}={\frac {\sum \limits _{n=0}^{\infty }{\frac {4(-1)^{n}}{2n+1}}}{\sum \limits _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n}}}}={\frac {{\frac {4}{1}}-{\frac {4}{3}}+{\frac {4}{5}}-{\frac {4}{7}}+{\frac {4}{9}}-\cdots }{{\frac {1}{1}}-{\frac {1}{2}}+{\frac {1}{3}}-{\frac {1}{4}}+{\frac {1}{5}}-\cdots }}}](//wikimedia.org/api/rest_v1/media/math/render/svg/926a668480e41169cfd1a0dabebd6f23e57c47ec) |
|
|
ਫਰਮਾ:OEIS2C |
[4;1,1,7,4,2,3,3,1,4,1,1,4,7,2,3,3,12,2,1,...] |
|
4.53236014182719380962768294571666681 |
0.76159 41559 55764 88811[Mw 11] |
Hyperbolic tangent of 1[13] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Hyperbolic_Tangent.svg/100px-Hyperbolic_Tangent.svg.png) |
![{\displaystyle {th}\,1}](//wikimedia.org/api/rest_v1/media/math/render/svg/f191f8f37d3482a5d9a85224fc6ec7694bc2921d) |
![{\displaystyle -i\tan(i)={\frac {e-{\frac {1}{e}}}{e+{\frac {1}{e}}}}={\frac {e^{2}-1}{e^{2}+1}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/02f2db6304490f7f71e836acf2198fc03891aa03) |
|
T |
ਫਰਮਾ:OEIS2C |
[0;1,3,5,7,9,11,13,15,17,19,21,23,25,27,...] = [0;2p+1], p∈ℕ |
|
0.76159415595576488811945828260479359 |
0.59017 02995 08048 11302[Mw 12] |
Chebyshev constant[14] · [15] |
|
![{\displaystyle {\lambda _{Ch}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/7cd3e5b10eb2807f472776b45b4611eeceebfeb8) |
![{\displaystyle {\frac {\Gamma ({\tfrac {1}{4}})^{2}}{4\pi ^{3/2}}}={\frac {4({\tfrac {1}{4}}!)^{2}}{\pi ^{3/2}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/14172a4ba8ec351156486f4e538531edc38af25c) |
(Gamma(1/4)^2)
/(4 pi^(3/2))
|
|
ਫਰਮਾ:OEIS2C |
[0;1,1,2,3,1,2,41,1,6,5,124,5,2,2,1,1,6,1,2,...] |
|
0.59017029950804811302266897027924429 |
0.07077 60393 11528 80353
-0.68400 03894 37932 129 i[Ow 1] |
MKB constant [16] · [17] · [18] |
|
![{\displaystyle M_{I}}](//wikimedia.org/api/rest_v1/media/math/render/svg/e18c7c1999cad7cbaf12b3059040dc89c2031415) |
![{\displaystyle \lim _{n\rightarrow \infty }\int _{1}^{2n}(-1)^{x}~{\sqrt[{x}]{x}}~dx=\int _{1}^{2n}e^{i\pi x}~x^{1/x}~dx}](//wikimedia.org/api/rest_v1/media/math/render/svg/d8a5f7620cf389898c275ed984f8688bbdf200b1) |
lim_(2n->∞) int[1 to 2n]
{exp(i*Pi*x)*x^(1/x) dx}
|
C |
ਫਰਮਾ:OEIS2C ਫਰਮਾ:OEIS2C |
[0;14,7,1,2,1,23,2,1,8,16,1,1,3,1,26,1,6,1,1, ...] - [0;1,2,6,13,41,112,1,25,1,1,1,1,3,13,2,1, ...] i |
2009 |
0.07077603931152880353952802183028200 -0.68400038943793212918274445999266 i |
1.25992 10498 94873 16476[Mw 13] |
Cube root of 2 Delian Constant |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Riemann_surface_cube_root.jpg/100px-Riemann_surface_cube_root.jpg) |
![{\displaystyle {\sqrt[{3}]{2}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/9ca071ab504481c2bb76081aacb03f5519930710) |
![{\displaystyle {\sqrt[{3}]{2}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/9ca071ab504481c2bb76081aacb03f5519930710) |
|
A |
ਫਰਮਾ:OEIS2C |
[1;3,1,5,1,1,4,1,1,8,1,14,1,10,2,1,4,12,2,3,...] |
|
1.25992104989487316476721060727822835 |
1.09317 04591 95490 89396[Mw 14] |
Smarandache Constant 1ª[19] |
|
![{\displaystyle {S_{1}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/b9ce95a04108d462df36dbb27308d88b928a692f) |
where μ(n) is the Kempner function |
|
|
ਫਰਮਾ:OEIS2C |
[1;10,1,2,1,2,1,13,3,1,6,1,2,11,4,6,2,15,1,1,...] |
|
1.09317045919549089396820137014520832 |
0.62481 05338 43826 58687 + 1.30024 25902 20120 419 i |
Generalized continued fraction of i |
|
![{\displaystyle {{F}_{CG}}_{(i)}}](//wikimedia.org/api/rest_v1/media/math/render/svg/421dac01b0478b2de142eca90422fb4163fdf916) |
![{\displaystyle \textstyle i{+}{\frac {i}{i+{\frac {i}{i+{\frac {i}{i+{\frac {i}{i+{\frac {i}{i+{\frac {i}{i+i{/...}}}}}}}}}}}}}={\sqrt {\frac {{\sqrt {17}}-1}{8}}}+i\left({\tfrac {1}{2}}{+}{\sqrt {\frac {2}{{\sqrt {17}}-1}}}\right)}](//wikimedia.org/api/rest_v1/media/math/render/svg/a9963d9be15a5593a95a78405cb4f5b28c905204) |
i+i/(i+i/(i+i/(i+i/(i+i/(
i+i/(i+i/(i+i/(i+i/(i+i/(
i+i/(i+i/(i+i/(i+i/(i+i/(
i+i/(i+i/(i+i/(i+i/(i+i/(
...)))))))))))))))))))))
|
C A |
ਫਰਮਾ:OEIS2C
ਫਰਮਾ:OEIS2C |
[i;1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,..] = [0;1,i] |
|
0.62481053384382658687960444744285144 + 1.30024259022012041915890982074952 i |
3.05940 74053 42576 14453[Mw 15][Ow 2] |
Double factorial constant |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Double_factorial.PNG/100px-Double_factorial.PNG) |
![{\displaystyle {C_{_{n!!}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/a3d46a3a8bb50a24b7844d1792ec5851029ef1e4) |
![{\displaystyle \sum _{n=0}^{\infty }{\frac {1}{n!!}}={\sqrt {e}}\left[{\frac {1}{\sqrt {2}}}+\gamma ({\tfrac {1}{2}},{\tfrac {1}{2}})\right]}](//wikimedia.org/api/rest_v1/media/math/render/svg/7e51ab5b1eae938ed34d7dd811be48e359de7b97) |
|
|
ਫਰਮਾ:OEIS2C |
[3;16,1,4,1,66,10,1,1,1,1,2,5,1,2,1,1,1,1,1,2,...] |
|
3.05940740534257614453947549923327861 |
5.97798 68121 78349 12266[Mw 16] |
Madelung Constant 2[20] |
|
![{\displaystyle {H}_{2}(2)}](//wikimedia.org/api/rest_v1/media/math/render/svg/507597e8a02be56eaba2108c76b19ae0518c3fc8) |
![{\displaystyle \pi \ln(3){\sqrt {3}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/d999d464d15c3b766d11627b310c8c897b7f8fce) |
|
|
ਫਰਮਾ:OEIS2C |
[5;1,44,2,2,1,15,1,1,12,1,65,11,1,3,1,1,...] |
|
5.97798681217834912266905331933922774 |
0.91893 85332 04672 74178[Mw 17] |
Raabe's formula[21] |
|
![{\displaystyle {\zeta '(0)}}](//wikimedia.org/api/rest_v1/media/math/render/svg/e5dc95fb415ec64d21b574cfd596456572a6064d) |
![{\displaystyle \int \limits _{a}^{a+1}\log \Gamma (t)\,\mathrm {d} t={\tfrac {1}{2}}\log 2\pi +a\log a-a,\quad a\geq 0}](//wikimedia.org/api/rest_v1/media/math/render/svg/07c4513d8e678eaa6b713e1e0c6a00293b464ebe) |
integral_a^(a+1)
{log(Gamma(x))+a-a log(a)} dx
|
|
ਫਰਮਾ:OEIS2C |
[0;1,11,2,1,36,1,1,3,3,5,3,1,18,2,1,1,2,2,1,1,...] |
|
0.91893853320467274178032973640561763 |
2.20741 60991 62477 96230[Mw 18] |
Lower limit in the moving sofa problem[22] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Hammersley_sofa_animated.gif/100px-Hammersley_sofa_animated.gif) |
![{\displaystyle {S_{_{H}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/3ea8fd5adef71bbe83378c65d3aa1a4b3fa26123) |
![{\displaystyle {\frac {\pi }{2}}+{\frac {2}{\pi }}}](//wikimedia.org/api/rest_v1/media/math/render/svg/c71f18dae5891f1fd056a4558b7f6d02e0842202) |
|
T |
ਫਰਮਾ:OEIS2C |
[2;4,1,4,1,1,2,5,1,11,1,1,5,1,6,1,3,1,1,1,1,7,...] |
1967 |
2.20741609916247796230685674512980889 |
1.17628 08182 59917 50654[Mw 19] |
Salem number,[23]
Lehmer's conjecture |
|
![{\displaystyle {\sigma _{_{10}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/3a23143f9ff2a5a1301fbef9cd3d35b5e0c5d826) |
![{\displaystyle x^{10}+x^{9}-x^{7}-x^{6}-x^{5}-x^{4}-x^{3}+x+1}](//wikimedia.org/api/rest_v1/media/math/render/svg/7f9fe49f4c74be3dc6b19075fae859422b34c558) |
x^10+x^9-x^7-x^6
-x^5-x^4-x^3+x+1
|
A |
ਫਰਮਾ:OEIS2C |
[1;5,1,2,17,1,7,2,1,1,2,4,7,2,2,1,1,15,1,1, ... |
1983? |
1.17628081825991750654407033847403505 |
0.37395 58136 19202 28805[Mw 20] |
Artin constant[24] |
|
![{\displaystyle {C}_{Artin}}](//wikimedia.org/api/rest_v1/media/math/render/svg/2eeb5f50208bb3bab84e8b6fddcefa95a28188e2) |
![{\displaystyle \prod _{n=1}^{\infty }\left(1-{\frac {1}{p_{n}(p_{n}-1)}}\right)\quad p_{n}\scriptstyle {\text{ = prime}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/bd65f5412c2e93e0a72dafda88bc6df7f6eabc83) |
Prod[n=1 to ∞]
{1-1/(prime(n)
(prime(n)-1))}
|
|
ਫਰਮਾ:OEIS2C |
[0;2,1,2,14,1,1,2,3,5,1,3,1,5,1,1,2,3,5,46,...] |
1999 |
0.37395581361920228805472805434641641 |
0.42215 77331 15826 62702[Mw 21] |
Volume of Reuleaux tetrahedron[25] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/4/44/ReuleauxTetrahedron_Animation.gif/100px-ReuleauxTetrahedron_Animation.gif) |
![{\displaystyle {V_{_{R}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/e0ccacd7ca0304c59ed711220f5aeecf1860f4b0) |
![{\displaystyle {\frac {s^{3}}{12}}(3{\sqrt {2}}-49\,\pi +162\,\arctan {\sqrt {2}})}](//wikimedia.org/api/rest_v1/media/math/render/svg/b9ccbcf13106ce50e8be2aec34f63ed88cc135a3) |
(3*Sqrt[2] - 49*Pi + 162*ArcTan[Sqrt[2]])/12
|
|
ਫਰਮਾ:OEIS2C |
[0;2,2,1,2,2,7,4,4,287,1,6,1,2,1,8,5,1,1,1,1, ...] |
|
0.42215773311582662702336591662385075 |
2.82641 99970 67591 57554[Mw 22] |
Murata Constant[26] |
|
![{\displaystyle {C_{m}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/51a666cc3a4b85452ed22d1e81fc73884dbc7a8b) |
![{\displaystyle \prod _{n=1}^{\infty }{\underset {p_{n}:\,{prime}}{{\Big (}1+{\frac {1}{(p_{n}-1)^{2}}}{\Big )}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/a84ded69c7faba9ea33f1751f0a06822c296547f) |
Prod[n=1 to ∞]
{1+1/(prime(n)
-1)^2}
|
|
ਫਰਮਾ:OEIS2C |
[2;1,4,1,3,5,2,2,2,4,3,2,1,3,2,1,1,1,8,2,2,28,...] |
|
2.82641999706759157554639174723695374 |
1.09864 19643 94156 48573[Mw 23] |
Paris Constant |
|
![{\displaystyle C_{Pa}}](//wikimedia.org/api/rest_v1/media/math/render/svg/fce63489d0798bb700f7490ab912b7b843a02f18) |
con y ![{\displaystyle \varphi _{1}{=}1}](//wikimedia.org/api/rest_v1/media/math/render/svg/639d57a62aadce6649e8791096cff33c6d32166e) |
|
|
ਫਰਮਾ:OEIS2C |
[1;10,7,3,1,3,1,5,1,4,2,7,1,2,3,22,1,2,5,2,1,...] |
|
1.09864196439415648573466891734359621 |
2.39996 32297 28653 32223[Mw 24] Radians |
Golden angle[27] |
![](//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Golden_Angle.svg/50px-Golden_Angle.svg.png) ![](//upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Sunflower.svg/50px-Sunflower.svg.png) |
![{\displaystyle {b}}](//wikimedia.org/api/rest_v1/media/math/render/svg/63ab20994dd08a611c5b5e257af5c72954cfaedb) |
= 137.5077640500378546 ...° |
|
T |
ਫਰਮਾ:OEIS2C |
[2;2,1,1,1087,4,4,120,2,1,1,2,1,1,7,7,2,11,...] |
1907 |
2.39996322972865332223155550663361385 |
1.64218 84352 22121 13687[Mw 25] |
Lebesgue constant L2[28] |
|
![{\displaystyle {L2}}](//wikimedia.org/api/rest_v1/media/math/render/svg/b4e964932505d69b188a2bb7589f7a6a9a8a9814) |
![{\displaystyle {\frac {1}{5}}+{\frac {\sqrt {25-2{\sqrt {5}}}}{\pi }}={\frac {1}{\pi }}\int _{0}^{\pi }{\frac {\left|\sin({\frac {5t}{2}})\right|}{\sin({\frac {t}{2}})}}\,dt}](//wikimedia.org/api/rest_v1/media/math/render/svg/32ad8d5821e4b56ca41ee4ec16d2d961badb36ba) |
1/5 + sqrt(25 -
2*sqrt(5))/Pi
|
T |
ਫਰਮਾ:OEIS2C |
[1;1,1,1,3,1,6,1,5,2,2,3,1,2,7,1,3,5,2,2,1,1,...] |
1910 |
1.64218843522212113687362798892294034 |
1.26408 47353 05301 11307[Mw 26] |
Vardi constant[29] |
|
![{\displaystyle {V_{c}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/890cb9bcba4e45dcdd365c8bb8c005bf9b074312) |
![{\displaystyle {\frac {\sqrt {3}}{\sqrt {2}}}\prod _{n\geq 1}\left(1+{1 \over (2e_{n}-1)^{2}}\right)^{\!1/2^{n+1}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/4019f55c7773c21a09657e1d04cebacc1ee1bd92) |
|
|
ਫਰਮਾ:OEIS2C |
[1;3,1,3,1,2,5,54,7,1,2,1,2,3,15,1,2,1,1,2,1,...] |
1991 |
1.26408473530530111307959958416466949 |
1.5065918849 ± 0.0000000028[Mw 27] |
Area of the Mandelbrot fractal[30] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Mandelbrot_sequence_new.gif/100px-Mandelbrot_sequence_new.gif) |
![{\displaystyle \gamma }](//wikimedia.org/api/rest_v1/media/math/render/svg/a223c880b0ce3da8f64ee33c4f0010beee400b1a) |
This is conjectured to be: ![{\displaystyle {\sqrt {6\pi -1}}-e=1.506591651\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/ae4bbd8e8f2f10187a437cbd4e7dc62234efb7eb) |
|
|
ਫਰਮਾ:OEIS2C |
[1;1,1,37,2,2,1,10,1,1,2,2,4,1,1,1,1,5,4,...] |
1912 |
1.50659177 +/- 0.00000008 |
1.61111 49258 08376 736 111···111 27224 36828[Mw 28] 183213 ones |
Exponential factorial constant |
|
![{\displaystyle {S_{Ef}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/acf819ac56489c76448f6cc018233acd0cc48edd) |
![{\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n^{(n{-}1)^{\cdot ^{\cdot ^{\cdot ^{2^{1}}}}}}}}=1{+}{\frac {1}{2^{1}}}{+}{\frac {1}{3^{2^{1}}}}+{\frac {1}{4^{3^{2^{1}}}}}+{\frac {1}{5^{4^{3^{2^{1}}}}}}{+}\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/6ab0f622dd687d9c8b629161a9d53fa816b55a62) |
|
T |
ਫਰਮਾ:OEIS2C |
[1; 1, 1, 1, 1, 2, 1, 808, 2, 1, 2, 1, 14,...] |
|
1.61111492580837673611111111111111111 |
1.11786 41511 89944 97314[Mw 29] |
Goh-Schmutz constant[31] |
|
![{\displaystyle C_{GS}}](//wikimedia.org/api/rest_v1/media/math/render/svg/62e109c1d7bb427f3a33fcbbc8c0ff86f23a71c6) |
|
Integrate{
log(s+1)
/(E^s-1)}
|
|
ਫਰਮਾ:OEIS2C |
[1;8,2,15,2,7,2,1,1,1,1,2,3,5,3,5,1,1,4,13,1,...] |
|
1.11786415118994497314040996202656544 |
0.31813 15052 04764 13531
±1.33723 57014 30689 40 i[Ow 3] |
Fixed points Super-Logarithm[32] · Tetration |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Slogez01.jpg/100px-Slogez01.jpg) |
![{\displaystyle {-W(-1)}}](//wikimedia.org/api/rest_v1/media/math/render/svg/f8737cfeb551bdce12941857768281d91ca5623c) |
![{\displaystyle \lim _{n\rightarrow \infty }}](//wikimedia.org/api/rest_v1/media/math/render/svg/f2aafb8c6824cedee3ae47f903afa07e4e06e6a7)
For an initial value of x different to , etc. |
-W(-1)
where W=ProductLog
Lambert W function |
C |
ਫਰਮਾ:OEIS2C ਫਰਮਾ:OEIS2C |
[-i;1 +2i,1+i,6-i,1+2i,-7+3i,2i,2,1-2i,-1+i,-, ...] |
|
0.31813150520476413531265425158766451 -1.33723570143068940890116214319371 i |
0.28016 94990 23869 13303[Mw 30] |
Bernstein's constant[33] |
|
![{\displaystyle {\beta }}](//wikimedia.org/api/rest_v1/media/math/render/svg/4f08e5bb6adcac8ac464df79e6a2e43779898ab7) |
![{\displaystyle \approx {\frac {1}{2{\sqrt {\pi }}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/a03ea768dbbf7435158b68bb34d01b2e48742e4c) |
|
T |
ਫਰਮਾ:OEIS2C |
[0;3,1,1,3,9,6,3,1,3,14,34,2,1,1,60,2,2,1,1,...] |
1913 |
0.28016949902386913303643649123067200 |
0.66016 18158 46869 57392[Mw 31] |
Twin Primes Constant[34] |
|
![{\displaystyle {C}_{2}}](//wikimedia.org/api/rest_v1/media/math/render/svg/d3e1dba7bf7becb3b2e64859163646499ab2e9b3) |
![{\displaystyle \prod _{p=3}^{\infty }{\frac {p(p-2)}{(p-1)^{2}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/383e9c2c21f24ac60752d1ce5239d105288a9710) |
prod[p=3 to ∞]
{p(p-2)/(p-1)^2
|
|
ਫਰਮਾ:OEIS2C |
[0;1,1,1,16,2,2,2,2,1,18,2,2,11,1,1,2,4,1,...] |
1922 |
0.66016181584686957392781211001455577 |
1.22674 20107 20353 24441[Mw 32] |
Fibonacci Factorial constant[35] |
|
![{\displaystyle F}](//wikimedia.org/api/rest_v1/media/math/render/svg/545fd099af8541605f7ee55f08225526be88ce57) |
![{\displaystyle \prod _{n=1}^{\infty }\left(1-\left(-{\frac {1}{{\varphi }^{2}}}\right)^{n}\right)=\prod _{n=1}^{\infty }\left(1-\left({\frac {{\sqrt {5}}-3}{2}}\right)^{n}\right)}](//wikimedia.org/api/rest_v1/media/math/render/svg/42c70a20140fb9313c8a53d931c0ee63f8bca365) |
prod[n=1 to ∞]
{1-((sqrt(5) -3)/2)^n}
|
|
ਫਰਮਾ:OEIS2C |
[1;4,2,2,3,2,15,9,1,2,1,2,15,7,6,21,3,5,1,23,...] |
|
1.22674201072035324441763023045536165 |
0.11494 20448 53296 20070[Mw 33] |
Kepler–Bouwkamp constant[36] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Regular_polygons_qtl4.svg/100px-Regular_polygons_qtl4.svg.png) |
![{\displaystyle {\rho }}](//wikimedia.org/api/rest_v1/media/math/render/svg/64fb820236ade4de4867d2ed7a0ff90ba32a5c6f) |
![{\displaystyle \prod _{n=3}^{\infty }\cos \left({\frac {\pi }{n}}\right)=\cos \left({\frac {\pi }{3}}\right)\cos \left({\frac {\pi }{4}}\right)\cos \left({\frac {\pi }{5}}\right)...}](//wikimedia.org/api/rest_v1/media/math/render/svg/1928e8aa498353f316079e65b69d29208e01e9af) |
prod[n=3 to ∞]
{cos(pi/n)}
|
|
ਫਰਮਾ:OEIS2C |
[0;8,1,2,2,1,272,2,1,41,6,1,3,1,1,26,4,1,1,...] |
|
0.11494204485329620070104015746959874 |
1.78723 16501 82965 93301[Mw 34] |
Komornik–Loreti constant[37] |
|
![{\displaystyle {q}}](//wikimedia.org/api/rest_v1/media/math/render/svg/203cc1519a2ceb65692e0836a9438b669100b475) |
tk = Thue–Morse sequence |
FindRoot[(prod[n=0 to ∞]
{1-1/(x^2^n)}+(x-2)
/(x-1))= 0, {x, 1.7},
WorkingPrecision->30]
|
T |
ਫਰਮਾ:OEIS2C |
[1;1,3,1,2,3,188,1,12,1,1,22,33,1,10,1,1,7,...] |
1998 |
1.78723165018296593301327489033700839 |
3.30277 56377 31994 64655[Mw 35] |
Bronze ratio[38] |
|
![{\displaystyle {\sigma }_{\,Rr}}](//wikimedia.org/api/rest_v1/media/math/render/svg/cdc379970038c176b9b848d37a314c3ad47a2879) |
![{\displaystyle {\frac {3+{\sqrt {13}}}{2}}=1+{\sqrt {3+{\sqrt {3+{\sqrt {3+{\sqrt {3+\cdots }}}}}}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/1ddb35544b4cbfede128a564d9af83f5fbb9d438) |
|
A |
ਫਰਮਾ:OEIS2C |
[3;3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,...] = [3;3,...] |
|
3.30277563773199464655961063373524797 |
0.82699 33431 32688 07426[Mw 36] |
Disk Covering[39] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/COVER5.gif/100px-COVER5.gif) |
![{\displaystyle {C_{5}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/aae22c5ce775e501d4ace78ae38ecc393742e3a5) |
![{\displaystyle {\frac {1}{\sum \limits _{n=0}^{\infty }{\frac {1}{\binom {3n+2}{2}}}}}={\frac {3{\sqrt {3}}}{2\pi }}}](//wikimedia.org/api/rest_v1/media/math/render/svg/eca0dd5bf37979703b9e2d314bb6d90a3d3537a1) |
|
T |
ਫਰਮਾ:OEIS2C |
[0;1,4,1,3,1,1,4,1,2,2,1,1,7,1,4,4,2,1,1,1,1,...] |
1939 1949 |
0.82699334313268807426698974746945416 |
2.66514 41426 90225 18865[Mw 37] |
Gelfond–Schneider constant[40] |
|
![{\displaystyle G_{\,GS}}](//wikimedia.org/api/rest_v1/media/math/render/svg/3a2107c9fb1a9149e6f8d8dfffb183150e2abaaf) |
![{\displaystyle 2^{\sqrt {2}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/2fe00689bdab9da3d6cd6015ca5e26c5702eaf22) |
|
T |
ਫਰਮਾ:OEIS2C |
[2;1,1,1,72,3,4,1,3,2,1,1,1,14,1,2,1,1,3,1,...] |
1934 |
2.66514414269022518865029724987313985 |
3.27582 29187 21811 15978[Mw 38] |
Khinchin-Lévy constant[41] |
|
![{\displaystyle \gamma }](//wikimedia.org/api/rest_v1/media/math/render/svg/a223c880b0ce3da8f64ee33c4f0010beee400b1a) |
![{\displaystyle e^{\pi ^{2}/(12\ln 2)}}](//wikimedia.org/api/rest_v1/media/math/render/svg/d03e1ae8e3320f65ee07c675959e57088872c07d) |
|
|
ਫਰਮਾ:OEIS2C |
[3;3,1,1,1,2,29,1,130,1,12,3,8,2,4,1,3,55,...] |
1936 |
3.27582291872181115978768188245384386 |
0.52382 25713 89864 40645[Mw 39] |
Chi Function Hyperbolic cosine integral |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Chi_function.png/100px-Chi_function.png) |
![{\displaystyle {\operatorname {Chi()} }}](//wikimedia.org/api/rest_v1/media/math/render/svg/25f6338b8fb68d8da09d31e828d66c2e735767a1) |
![{\displaystyle \scriptstyle \gamma \,{\text{= Euler–Mascheroni constant= 0.5772156649...}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/9278dc8757e358bc603caf2a57d5e18600e75d72)
|
|
|
ਫਰਮਾ:OEIS2C |
[0;1,1,9,1,172,1,7,1,11,1,1,2,1,8,1,1,1,1,1,...] |
|
0.52382257138986440645095829438325566 |
1.13198 82487 943[Mw 40] |
Viswanath constant[42] |
|
![{\displaystyle {C}_{Vi}}](//wikimedia.org/api/rest_v1/media/math/render/svg/aa70ce5764371cae7ce73a8407ddd5f91778d580) |
where an = Fibonacci sequence |
|
T ? |
ਫਰਮਾ:OEIS2C |
[1;7,1,1,2,1,3,2,1,2,1,8,1,5,1,1,1,9,1,...] |
1997 |
1.1319882487943 ... |
1.23370 05501 36169 82735[Mw 41] |
Favard constant[43] |
|
![{\displaystyle {\tfrac {3}{4}}\zeta (2)}](//wikimedia.org/api/rest_v1/media/math/render/svg/fe9728f82b8da0010c93594d16050ba73b3a9c59) |
![{\displaystyle {\frac {\pi ^{2}}{8}}=\sum _{n=0}^{\infty }{\frac {1}{(2n-1)^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}+\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/e0d337132ebe491dd613d33fedf51b83407bc88e) |
sum[n=1 to ∞]
{1/((2n-1)^2)}
|
T |
ਫਰਮਾ:OEIS2C |
[1;4,3,1,1,2,2,5,1,1,1,1,2,1,2,1,10,4,3,1,1,...] |
1902 a 1965 |
1.23370055013616982735431137498451889 |
2.50662 82746 31000 50241 |
Square root of 2 pi |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Stirling%27s_Approximation_Small.png/100px-Stirling%27s_Approximation_Small.png) |
![{\displaystyle {\sqrt {2\pi }}}](//wikimedia.org/api/rest_v1/media/math/render/svg/7a9b009153bbbb3273a7e7279cb6b084fd650a80) |
Stirling's approximation |
|
T |
ਫਰਮਾ:OEIS2C |
[2;1,1,37,4,1,1,1,1,9,1,1,2,8,6,1,2,2,1,3,...] |
1692 a 1770 |
2.50662827463100050241576528481104525 |
4.13273 13541 22492 93846 |
Square root of Tau·e |
|
![{\displaystyle {\sqrt {\tau e}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/491b3fd5508d94821c56cc61e25d81f51735f5ea) |
![{\displaystyle {\sqrt {2\pi e}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/104d77d9773f551bd9d87b92158553fdd6ccbc9f) |
|
|
ਫਰਮਾ:OEIS2C |
[4;7,1,1,6,1,5,1,1,1,8,3,1,2,2,15,2,1,1,2,4,...] |
|
4.13273135412249293846939188429985264 |
0.97027 01143 92033 92574[Mw 42] |
Lochs constant[44] |
|
![{\displaystyle {{\text{£}}_{_{Lo}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/06bf3db99d2e1cc5127b24cd2ac6e7e720156de3) |
![{\displaystyle {\frac {6\ln 2\ln 10}{\pi ^{2}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/3c7ff8ab71c7344335d4a9f1a7c8241b55f26a99) |
|
|
ਫਰਮਾ:OEIS2C |
[0;1,32,1,1,1,2,1,46,7,2,7,10,8,1,71,1,37,1,1,...] |
1964 |
0.97027011439203392574025601921001083 |
0.98770 03907 36053 46013[Mw 43] |
Area bounded by the eccentric rotation of Reuleaux triangle[45] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Rotation_of_Reuleaux_triangle.gif/100px-Rotation_of_Reuleaux_triangle.gif) |
![{\displaystyle {\mathcal {T}}_{R}}](//wikimedia.org/api/rest_v1/media/math/render/svg/4a1b19e33b17b73085a350017b10fb6ef95d0256) |
where a= side length of the square |
|
T |
ਫਰਮਾ:OEIS2C |
[0;1,80,3,3,2,1,1,1,4,2,2,1,1,1,8,1,2,10,1,2,...] |
1914 |
0.98770039073605346013199991355832854 |
0.70444 22009 99165 59273 |
Carefree constant 2[46] |
|
![{\displaystyle {\mathcal {C}}_{2}}](//wikimedia.org/api/rest_v1/media/math/render/svg/e5e4f90850fb306af575d9a4a37b15b6d9178ce2) |
![{\displaystyle {\underset {p_{n}:\,{prime}}{\prod _{n=1}^{\infty }\left(1-{\frac {1}{p_{n}(p_{n}+1)}}\right)}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/264ca3dbc16dc87b7a880aae5692ff618d8bde45) |
N[prod[n=1 to ∞]
{1 - 1/(prime(n)*
(prime(n)+1))}]
|
|
ਫਰਮਾ:OEIS2C |
[0;1,2,2,1,1,1,1,4,2,1,1,3,703,2,1,1,1,3,5,1,...] |
|
0.70444220099916559273660335032663721 |
1.84775 90650 22573 51225[Mw 44] |
Connective constant[47][48] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/HEX-LATTICE-20.gif/100px-HEX-LATTICE-20.gif) |
![{\displaystyle {\mu }}](//wikimedia.org/api/rest_v1/media/math/render/svg/fb2e32303f97e0988fc733de21d8fb57cc12360f) |
as a root of the polynomial :\;x^{4}-4x^{2}+2=0}
![{\displaystyle :\;x^{4}-4x^{2}+2=0}](//wikimedia.org/api/rest_v1/media/math/render/svg/a9cb86e550322bfc74feb0b6f133f8977d34bcba) |
|
A |
ਫਰਮਾ:OEIS2C |
[1;1,5,1,1,3,6,1,3,3,10,10,1,1,1,5,2,3,1,1,3,...] |
|
1.84775906502257351225636637879357657 |
0.30366 30028 98732 65859[Mw 45] |
Gauss-Kuzmin-Wirsing constant[49] |
|
![{\displaystyle {\lambda }_{2}}](//wikimedia.org/api/rest_v1/media/math/render/svg/0f9237e9d42d3fef2469dda0cd0c98e69216a53e) |
where is an analytic function with . |
|
|
ਫਰਮਾ:OEIS2C |
[0;3,3,2,2,3,13,1,174,1,1,1,2,2,2,1,1,1,2,2,1,...] |
1973 |
0.30366300289873265859744812190155623 |
1.57079 63267 94896 61923[Mw 46] |
Favard constant K1 Wallis product[50] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/9/9b/Wallis_product-chart.png/100px-Wallis_product-chart.png) |
![{\displaystyle {\frac {\pi }{2}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/98f98bef5d4981ff6e2aa827d4699e347fb30db2) |
![{\displaystyle \prod _{n=1}^{\infty }\left({\frac {4n^{2}}{4n^{2}-1}}\right)={\frac {2}{1}}\cdot {\frac {2}{3}}\cdot {\frac {4}{3}}\cdot {\frac {4}{5}}\cdot {\frac {6}{5}}\cdot {\frac {6}{7}}\cdot {\frac {8}{7}}\cdot {\frac {8}{9}}\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/db44a63fee4d571657b2faccb0dd2f5b6232e234) |
Prod[n=1 to ∞]
{(4n^2)/(4n^2-1)}
|
T |
ਫਰਮਾ:OEIS2C |
[1;1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,1,5,1...] |
1655 |
1.57079632679489661923132169163975144 |
1.60669 51524 15291 76378[Mw 47] |
Erdős–Borwein constant[51][52] |
|
![{\displaystyle {E}_{\,B}}](//wikimedia.org/api/rest_v1/media/math/render/svg/86243f55dde381ccbeed0f04dffc641e2d511e4f) |
![{\displaystyle \sum _{m=1}^{\infty }\sum _{n=1}^{\infty }{\frac {1}{2^{mn}}}=\sum _{n=1}^{\infty }{\frac {1}{2^{n}-1}}={\frac {1}{1}}\!+\!{\frac {1}{3}}\!+\!{\frac {1}{7}}\!+\!{\frac {1}{15}}\!+\!...}](//wikimedia.org/api/rest_v1/media/math/render/svg/ed135230607f732517d081d6f28467c81e780dfb) |
sum[n=1 to ∞]
{1/(2^n-1)}
|
I |
ਫਰਮਾ:OEIS2C |
[1;1,1,1,1,5,2,1,2,29,4,1,2,2,2,2,6,1,7,1,...] |
1949 |
1.60669515241529176378330152319092458 |
1.61803 39887 49894 84820[Mw 48] |
Phi, Golden ratio[53] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Animation_GoldenerSchnitt.gif/100px-Animation_GoldenerSchnitt.gif) |
![{\displaystyle {\varphi }}](//wikimedia.org/api/rest_v1/media/math/render/svg/af3cb274a1344747f5d71f51dc671d5b4acf26df) |
![{\displaystyle {\frac {1+{\sqrt {5}}}{2}}={\sqrt {1+{\sqrt {1+{\sqrt {1+{\sqrt {1+\cdots }}}}}}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/df2a3ad8ee12eadff65e59d16e3ef142ff86da3d) |
|
A |
ਫਰਮਾ:OEIS2C |
[0;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,...] = [0;1,...] |
-300 ~ |
1.61803398874989484820458683436563811 |
1.64493 40668 48226 43647[Mw 49] |
Riemann Function Zeta(2) |
|
![{\displaystyle {\zeta }(\,2)}](//wikimedia.org/api/rest_v1/media/math/render/svg/b85a516dd728f7ec6ce080054ffb2d683b281fc3) |
![{\displaystyle {\frac {\pi ^{2}}{6}}=\sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{4^{2}}}+\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/8bfdb12b6f3b53059219084bfe8821ece9a61c83) |
|
T |
ਫਰਮਾ:OEIS2C |
[1;1,1,1,4,2,4,7,1,4,2,3,4,10 1,2,1,1,1,15,...] |
1826 to 1866 |
1.64493406684822643647241516664602519 |
1.73205 08075 68877 29352[Mw 50] |
Theodorus constant[54] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Square_root_of_3_in_cube.svg/100px-Square_root_of_3_in_cube.svg.png) |
![{\displaystyle {\sqrt {3}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/3b19c09494138b5082459afac7f9a8d99c546fcd) |
![{\displaystyle {\sqrt[{3}]{3\,{\sqrt[{3}]{3\,{\sqrt[{3}]{3\,{\sqrt[{3}]{3\,{\sqrt[{3}]{3\,\cdots }}}}}}}}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/f6a7a7a3adada2776b2b2ade49205f1f22eafca1) |
(3(3(3(3(3(3(3)
^1/3)^1/3)^1/3)
^1/3)^1/3)^1/3)
^1/3 ...
|
A |
ਫਰਮਾ:OEIS2C |
[1;1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,...] = [1;1,2,...] |
-465 to -398 |
1.73205080756887729352744634150587237 |
1.75793 27566 18004 53270[Mw 51] |
Kasner number |
|
![{\displaystyle {R}}](//wikimedia.org/api/rest_v1/media/math/render/svg/3abe7f424f59ed9925c7f622af7aead87831412b) |
![{\displaystyle {\sqrt {1+{\sqrt {2+{\sqrt {3+{\sqrt {4+\cdots }}}}}}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/08adc1ee570a6b53344b2a64f1f88424e5549cbc) |
Fold[Sqrt[#1+#2]
&,0,Reverse
[Range[20]]]
|
|
ਫਰਮਾ:OEIS2C |
[1;1,3,7,1,1,1,2,3,1,4,1,1,2,1,2,20,1,2,2,...] |
1878 a 1955 |
1.75793275661800453270881963821813852 |
2.29558 71493 92638 07403[Mw 52] |
Universal parabolic constant[55] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Parabola_animada.gif/100px-Parabola_animada.gif) |
![{\displaystyle {P}_{\,2}}](//wikimedia.org/api/rest_v1/media/math/render/svg/d9c7592036b2e0b48ef116bce8b439980b42d6d4) |
![{\displaystyle \ln(1+{\sqrt {2}})+{\sqrt {2}}\;=\;\operatorname {arcsinh} (1)+{\sqrt {2}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/0edb48bcb1edecc3e8fe9bbb9128df56cf74412e) |
|
T |
ਫਰਮਾ:OEIS2C |
[2;3,2,1,1,1,1,3,3,1,1,4,2,3,2,7,1,6,1,8,7,2,1,...] |
|
2.29558714939263807403429804918949038 |
1.78657 64593 65922 46345[Mw 53] |
Silverman constant[56] |
|
![{\displaystyle {{\mathcal {S}}_{_{m}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/4447a8dd392e3dfdbb71ea57981c39bb60f5e19a) |
ø() = Euler's totient function, σ1() = Divisor function. |
Sum[n=1 to ∞]
{1/[EulerPhi(n)
DivisorSigma(1,n)]}
|
|
ਫਰਮਾ:OEIS2C |
[1;1,3,1,2,5,1,65,11,2,1,2,13,1,4,1,1,1,2,5,4,...] |
|
1.78657645936592246345859047554131575 |
2.59807 62113 53315 94029[Mw 54] |
Area of the regular hexagon with side equal to 1[57] |
| ![{\displaystyle {\mathcal {A}}_{6}}](//wikimedia.org/api/rest_v1/media/math/render/svg/0e3db115eb0afae9eec1c5c5da26bf7cb649c429) |
![{\displaystyle {\frac {3{\sqrt {3}}}{2}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/9470b40b0feddef627ee006d44eb5a98fab565f4) |
|
A |
ਫਰਮਾ:OEIS2C |
[2;1,1,2,20,2,1,1,4,1,1,2,20,2,1,1,4,1,1,2,20,...] [2;1,1,2,20,2,1,1,4] |
|
2.59807621135331594029116951225880855 |
0.66131 70494 69622 33528[Mw 55] |
Feller-Tornier constant[58] |
|
![{\displaystyle {{\mathcal {C}}_{_{FT}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/a9dd887ec7afdaa54a24f16be416cd22260c5692) |
![{\displaystyle {\underset {p_{n}:\,{prime}}{{\frac {1}{2}}\prod _{n=1}^{\infty }\left(1-{\frac {2}{p_{n}^{2}}}\right){+}{\frac {1}{2}}}}={\frac {3}{\pi ^{2}}}\prod _{n=1}^{\infty }\left(1-{\frac {1}{p_{n}^{2}-1}}\right){+}{\frac {1}{2}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/e1faaef1ecd05b1a090247186d1c6b2c325c8cf8) |
[prod[n=1 to ∞]
{1-2/prime(n)^2}]
/2 + 1/2
|
T ? |
ਫਰਮਾ:OEIS2C |
[0;1,1,1,20,9,1,2,5,1,2,3,2,3,38,8,1,16,2,2,...] |
1932 |
0.66131704946962233528976584627411853 |
1.46099 84862 06318 35815[Mw 56] |
Baxter's Four-coloring constant[59] |
Mapamundi Four-Coloring
| ![{\displaystyle {\mathcal {C}}^{2}}](//wikimedia.org/api/rest_v1/media/math/render/svg/86a81a0818245a818ce645f5c119f4caa9e805aa) |
Γ() = Gamma function |
|
|
ਫਰਮਾ:OEIS2C |
[1;2,5,1,10,8,1,12,3,1,5,3,5,8,2,1,23,1,2,161,...] |
1970 |
1.46099848620631835815887311784605969 |
1.92756 19754 82925 30426[Mw 57] |
Tetranacci constant
|
|
![{\displaystyle {\mathcal {T}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/8236d074e42310f5dc24d1d2b5b8f5981c3e87ba) |
Positive root of :\;\;x^{4}-x^{3}-x^{2}-x-1=0}
![{\displaystyle :\;\;x^{4}-x^{3}-x^{2}-x-1=0}](//wikimedia.org/api/rest_v1/media/math/render/svg/7fcfd2c07337421a2f2af01c8f6afee1082504e0) |
|
A |
ਫਰਮਾ:OEIS2C |
[1;1,12,1,4,7,1,21,1,2,1,4,6,1,10,1,2,2,1,7,1,...] |
|
1.92756197548292530426190586173662216 |
1.00743 47568 84279 37609[Mw 58] |
DeVicci's tesseract constant
|
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/8-cell-orig.gif/100px-8-cell-orig.gif) |
![{\displaystyle {f_{(3,4)}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/df709d9fea0d70f9959fa6363a794e2dc66c7d7c) |
The largest cube that can pass through in an 4D hypercube.
Positive root of :\;\;4x^{4}{-}28x^{3}{-}7x^{2}{+}16x{+}16=0}
![{\displaystyle :\;\;4x^{4}{-}28x^{3}{-}7x^{2}{+}16x{+}16=0}](//wikimedia.org/api/rest_v1/media/math/render/svg/5a39d48f84006c760fccbde9e22d398b018591ed) |
Root[4*x^8-28*x^6
-7*x^4+16*x^2+16
=0]
|
A |
ਫਰਮਾ:OEIS2C |
[1;134,1,1,73,3,1,5,2,1,6,3,11,4,1,5,5,1,1,48,...] |
|
1.00743475688427937609825359523109914 |
1.70521 11401 05367 76428[Mw 59] |
Niven's constant[60] |
|
![{\displaystyle {C}}](//wikimedia.org/api/rest_v1/media/math/render/svg/7d9247343616c7631c19c44d199b0e0fce1847ad) |
![{\displaystyle 1+\sum _{n=2}^{\infty }\left(1-{\frac {1}{\zeta (n)}}\right)}](//wikimedia.org/api/rest_v1/media/math/render/svg/b12c54be70e014bf76248e2dddc12cb80d1e23e6) |
1+ Sum[n=2 to ∞]
{1-(1/Zeta(n))}
|
|
ਫਰਮਾ:OEIS2C |
[1;1,2,2,1,1,4,1,1,3,4,4,8,4,1,1,2,1,1,11,1,...] |
1969 |
1.70521114010536776428855145343450816 |
0.60459 97880 78072 61686[Mw 60] |
Relationship among the area of an equilateral triangle and the inscribed circle. |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/a/af/Fano_plane.svg/100px-Fano_plane.svg.png) |
![{\displaystyle {\frac {\pi }{3{\sqrt {3}}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/9e87580f1fcf9c9b18a8e4a5d9261491e79b8bf8) |
Dirichlet series |
Sum[1/(n
Binomial[2 n, n])
, {n, 1, ∞}]
|
T |
ਫਰਮਾ:OEIS2C |
[0;1,1,1,1,8,10,2,2,3,3,1,9,2,5,4,1,27,27,6,6,...] |
|
0.60459978807807261686469275254738524 |
1.15470 05383 79251 52901[Mw 61] |
Hermite constant[61] |
|
![{\displaystyle \gamma _{_{2}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/b2723d3d687dda7186a3f6581411efcf8d5fffa1) |
![{\displaystyle {\frac {2}{\sqrt {3}}}={\frac {1}{\cos \,({\frac {\pi }{6}})}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/267eeb178a089d75bdf3dc94b6df2be75ae46f7f) |
|
A |
1+ ਫਰਮਾ:OEIS2C |
[1;6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,...] [1;6,2] |
|
1.15470053837925152901829756100391491 |
0.41245 40336 40107 59778[Mw 62] |
Prouhet–Thue–Morse constant[62] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Thue-MorseRecurrence.gif/100px-Thue-MorseRecurrence.gif) |
![{\displaystyle \tau }](//wikimedia.org/api/rest_v1/media/math/render/svg/38a7dcde9730ef0853809fefc18d88771f95206c) |
where is the Thue–Morse sequence and Where ![{\displaystyle \tau (x)=\sum _{n=0}^{\infty }(-1)^{t_{n}}\,x^{n}=\prod _{n=0}^{\infty }(1-x^{2^{n}})}](//wikimedia.org/api/rest_v1/media/math/render/svg/bb5c2972ad498674f5548be245addcada3b454c4) |
|
T |
ਫਰਮਾ:OEIS2C |
[0;2,2,2,1,4,3,5,2,1,4,2,1,5,44,1,4,1,2,4,1,1,...] |
|
0.41245403364010759778336136825845528 |
0.58057 75582 04892 40229[Mw 63] |
Pell constant[63] |
|
![{\displaystyle {{\mathcal {P}}_{_{Pell}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/60bea46738666b7ee192810e7e6edd0d373572ee) |
![{\displaystyle 1-\prod _{n=0}^{\infty }\left(1-{\frac {1}{2^{2n+1}}}\right)}](//wikimedia.org/api/rest_v1/media/math/render/svg/adea1115dc96fac4e4ea17c3a0684dd3e49db60b) |
N[1-prod[n=0 to ∞]
{1-1/(2^(2n+1)}]
|
T ? |
ਫਰਮਾ:OEIS2C |
[0;1,1,2,1,1,1,1,14,1,3,1,1,6,9,18,7,1,27,1,1,...] |
|
0.58057755820489240229004389229702574 |
0.66274 34193 49181 58097[Mw 64] |
Laplace limit[64] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Laplace_limit.png/100px-Laplace_limit.png) |
![{\displaystyle {\lambda }}](//wikimedia.org/api/rest_v1/media/math/render/svg/80912e657954ba7a08dc822fac02fd5fd61067c1) |
![{\displaystyle {\frac {x\;e^{\sqrt {x^{2}+1}}}{{\sqrt {x^{2}+1}}+1}}=1}](//wikimedia.org/api/rest_v1/media/math/render/svg/c01d7b4fded0011ea692b375026d87aa06500ae1) |
(x e^sqrt(x^2+1))
/(sqrt(x^2+1)+1) = 1
|
|
ਫਰਮਾ:OEIS2C |
[0;1,1,1,27,1,1,1,8,2,154,2,4,1,5,1,1,2,1601,...] |
1782 ~ |
0.66274341934918158097474209710925290 |
0.17150 04931 41536 06586[Mw 65] |
Hall-Montgomery Constant[65] |
|
![{\displaystyle {{\delta }_{_{0}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/efd7e203ab4f919612268101a027ff58d7323689) |
![{\displaystyle 1+{\frac {\pi ^{2}}{6}}+2\;\mathrm {Li} _{2}\left(-{\sqrt {e}}\;\right)\quad \mathrm {Li} _{2}\,\scriptstyle {\text{= Dilogarithm integral}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/a6b44ffe7860373ba3b0a226841c635c92ad5917) |
1 + Pi^2/6 +
2*PolyLog[2, -Sqrt[E]]
|
|
ਫਰਮਾ:OEIS2C |
[0;5,1,4,1,10,1,1,11,18,1,2,19,14,1,51,1,2,1,...] |
|
0.17150049314153606586043997155521210 |
1.55138 75245 48320 39226[Mw 66] |
Calabi triangle constant[66] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Calabi_triangle.svg/100px-Calabi_triangle.svg.png) |
![{\displaystyle {C_{_{CR}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/6523a0bfd999e8115fd405e54e046d56b01ab2ed) |
![{\displaystyle {1 \over 3}+{(-23+3i{\sqrt {237}})^{\tfrac {1}{3}} \over 3\cdot 2^{\tfrac {2}{3}}}+{11 \over 3(2(-23+3i{\sqrt {237}}))^{\tfrac {1}{3}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/8793fec68917c643859a20a7fc0eac25ad4e6acc) |
FindRoot[
2x^3-2x^2-3x+2
==0, {x, 1.5},
WorkingPrecision->40]
|
A |
ਫਰਮਾ:OEIS2C |
[1;1,1,4,2,1,2,1,5,2,1,3,1,1,390,1,1,2,11,6,2,...] |
1946 ~ |
1.55138752454832039226195251026462381 |
1.22541 67024 65177 64512[Mw 67] |
Gamma(3/4)[67] |
|
![{\displaystyle \Gamma ({\tfrac {3}{4}})}](//wikimedia.org/api/rest_v1/media/math/render/svg/eb60a6f7e1e0207383bcee95a04c5475dbc3e553) |
![{\displaystyle \left(-1+{\frac {3}{4}}\right)!=\left(-{\frac {1}{4}}\right)!}](//wikimedia.org/api/rest_v1/media/math/render/svg/2f4ba0cde2e7670eff0f3ddc661d48f0265b4a59) |
|
|
ਫਰਮਾ:OEIS2C |
[1;4,2,3,2,2,1,1,1,2,1,4,7,1,171,3,2,3,1,1,8,3,...] |
|
1.22541670246517764512909830336289053 |
1.20205 69031 59594 28539[Mw 68] |
Apéry's constant[68] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/8/84/Ap%C3%A9ry%27s_constant.svg/100px-Ap%C3%A9ry%27s_constant.svg.png) |
![{\displaystyle \zeta (3)}](//wikimedia.org/api/rest_v1/media/math/render/svg/3088978098c7b90b2754a9d9b0b994d873e1755c) |
![{\displaystyle {\frac {1}{2}}\sum _{n=1}^{\infty }{\frac {H_{n}}{n^{2}}}={\frac {1}{2}}\sum _{i=1}^{\infty }\sum _{j=1}^{\infty }{\frac {1}{ij(i{+}j)}}=\!\!\int \limits _{0}^{1}\!\!\int \limits _{0}^{1}\!\!\int \limits _{0}^{1}{\frac {\mathrm {d} x\mathrm {d} y\mathrm {d} z}{1-xyz}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/f8f4412d740a79f64e534cf8201933bd9add160d)
|
|
I |
ਫਰਮਾ:OEIS2C |
[1;4,1,18,1,1,1,4,1,9,9,2,1,1,1,2,7,1,1,7,11,...] |
1979 |
1.20205690315959428539973816151144999 |
0.91596 55941 77219 01505[Mw 69] |
Catalan's constant[69][70][71] |
|
![{\displaystyle {C}}](//wikimedia.org/api/rest_v1/media/math/render/svg/7d9247343616c7631c19c44d199b0e0fce1847ad) |
![{\displaystyle \int _{0}^{1}\!\!\int _{0}^{1}\!\!{\frac {1}{1{+}x^{2}y^{2}}}\,dx\,dy=\!\sum _{n=0}^{\infty }\!{\frac {(-1)^{n}}{(2n{+}1)^{2}}}\!=\!{\frac {1}{1^{2}}}{-}{\frac {1}{3^{2}}}{+}{\cdots }}](//wikimedia.org/api/rest_v1/media/math/render/svg/8a4cee4bea9194a3dee0960e2e3737818e17f034) |
Sum[n=0 to ∞]
{(-1)^n/(2n+1)^2}
|
T |
ਫਰਮਾ:OEIS2C |
[0;1,10,1,8,1,88,4,1,1,7,22,1,2,3,26,1,11,...] |
1864 |
0.91596559417721901505460351493238411 |
0.78539 81633 97448 30961[Mw 70] |
Beta(1)[72] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Loglogisticcdf.svg/100px-Loglogisticcdf.svg.png) |
![{\displaystyle {\beta }(1)}](//wikimedia.org/api/rest_v1/media/math/render/svg/f0deefab2bc57c0e1187875e3c377e4689417f78) |
![{\displaystyle {\frac {\pi }{4}}=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{2n+1}}={\frac {1}{1}}-{\frac {1}{3}}+{\frac {1}{5}}-{\frac {1}{7}}+{\frac {1}{9}}-\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/37ec4cad4251a0f8471f23758a9efbec5589117e) |
Sum[n=0 to ∞]
{(-1)^n/(2n+1)}
|
T |
ਫਰਮਾ:OEIS2C |
[0; 1,3,1,1,1,15,2,72,1,9,1,17,1,2,1,5,1,1,10,...] |
1805 to 1859 |
0.78539816339744830961566084581987572 |
0.00131 76411 54853 17810[Mw 71] |
Heath-Brown–Moroz constant[73] |
|
![{\displaystyle {C_{_{HBM}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/ebedb164109e386953b04046793b3cc0a9bcba01) |
![{\displaystyle {\underset {p_{n}:\,{prime}}{\prod _{n=1}^{\infty }\left(1-{\frac {1}{p_{n}}}\right)^{7}\left(1+{\frac {7p_{n}+1}{p_{n}^{2}}}\right)}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/6c8cb18eeeeb2c2d1d767777303b94dd79db19cf) |
N[prod[n=1 to ∞]
{((1-1/prime(n))^7)
*(1+(7*prime(n)+1)
/(prime(n)^2))}]
|
T ? |
ਫਰਮਾ:OEIS2C |
[0;758,1,13,1,2,3,56,8,1,1,1,1,1,143,1,1,1,2,...] |
|
0.00131764115485317810981735232251358 |
0.56755 51633 06957 82538 |
Module of ।nfinite Tetration of i |
|
![{\displaystyle |{}^{\infty }{i}|}](//wikimedia.org/api/rest_v1/media/math/render/svg/75c858b5a20f4bc51e1a8a9d81dc77f7975dedce) |
![{\displaystyle \lim _{n\to \infty }\left|{}^{n}i\right|=\left|\lim _{n\to \infty }\underbrace {i^{i^{\cdot ^{\cdot ^{i}}}}} _{n}\right|}](//wikimedia.org/api/rest_v1/media/math/render/svg/bd71af7c46dba4847f193ac4e9a6fbeda7c6b351) |
|
|
ਫਰਮਾ:OEIS2C |
[0;1,1,3,4,1,58,12,1,51,1,4,12,1,1,2,2,3,...] |
|
0.56755516330695782538461314419245334 |
0.78343 05107 12134 40705[Mw 72] |
Sophomore's dream1 J.Bernoulli[74] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/3/39/Reve_etudiant.svg/100px-Reve_etudiant.svg.png) |
![{\displaystyle {I}_{1}}](//wikimedia.org/api/rest_v1/media/math/render/svg/546dbad826cad4457dc501ab6fb4ede20b2f2b7a) |
![{\displaystyle \int _{0}^{1}\!x^{x}\,dx=\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{n}}}={\frac {1}{1^{1}}}-{\frac {1}{2^{2}}}+{\frac {1}{3^{3}}}-{\cdots }}](//wikimedia.org/api/rest_v1/media/math/render/svg/89ee6330a6cbf73d530b8bfb057a31bc28374c49) |
Sum[n=1 to ∞]
{-(-1)^n /n^n}
|
|
ਫਰਮਾ:OEIS2C |
[0;1,3,1,1,1,1,1,1,2,4,7,2,1,2,1,1,1,2,1,14,...] |
1697 |
0.78343051071213440705926438652697546 |
1.29128 59970 62663 54040[Mw 73] |
Sophomore's dream2 J.Bernoulli[75] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Socd_001.png/100px-Socd_001.png) |
![{\displaystyle {I}_{2}}](//wikimedia.org/api/rest_v1/media/math/render/svg/2473baaa3aae71dc3ed77912b2298610c35d5846) |
![{\displaystyle \int _{0}^{1}\!{\frac {1}{x^{x}}}\,dx=\sum _{n=1}^{\infty }{\frac {1}{n^{n}}}={\frac {1}{1^{1}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{3}}}+{\frac {1}{4^{4}}}+\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/f437d46ecb9d999bbbc0df3e73c89e62222598f6) |
|
|
ਫਰਮਾ:OEIS2C |
[1;3,2,3,4,3,1,2,1,1,6,7,2,5,3,1,2,1,8,1,2,4,...] |
1697 |
1.29128599706266354040728259059560054 |
0.70523 01717 91800 96514[Mw 74] |
Primorial constant Sum of the product of inverse of primes [76] |
|
![{\displaystyle {P_{\#}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/fea919fced2e18d73c392c62e7ec8138f532d6c1) |
![{\displaystyle {\underset {p_{n}:\,{prime}}{\sum _{n=1}^{\infty }{\frac {1}{p_{n}\#}}={\frac {1}{2}}+{\frac {1}{6}}+{\frac {1}{30}}+{\frac {1}{210}}+...=\sum _{k=1}^{\infty }\prod _{n=1}^{k}{\frac {1}{p_{n}}}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/c57e81afceb2ca07a2b8e1116dcf99c4e4304193) |
Sum[k=1 to ∞]
(prod[n=1 to k]
{1/prime(n)})
|
I |
ਫਰਮਾ:OEIS2C |
[0;1,2,2,1,1,4,1,2,1,1,6,13,1,4,1,16,6,1,1,4,...] |
|
0.70523017179180096514743168288824851 |
0.14758 36176 50433 27417[Mw 75] |
Plouffe's gamma constant[77] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Trigo-arctan-animation.gif/100px-Trigo-arctan-animation.gif) |
![{\displaystyle {C}}](//wikimedia.org/api/rest_v1/media/math/render/svg/7d9247343616c7631c19c44d199b0e0fce1847ad) |
![{\displaystyle {\frac {1}{\pi }}\arctan {\frac {1}{2}}={\frac {1}{\pi }}\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2^{2n+1})(2n+1)}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/eef66b38dfd37cdea5ce647f9892cc563a0d2297)
![{\displaystyle ={\frac {1}{\pi }}\left({\frac {1}{2}}-{\frac {1}{3\cdot 2^{3}}}+{\frac {1}{5\cdot 2^{5}}}-{\frac {1}{7\cdot 2^{7}}}+\cdots \right)}](//wikimedia.org/api/rest_v1/media/math/render/svg/c5e1e5c8045af1cd186a7da95702095097f61342) |
|
T |
ਫਰਮਾ:OEIS2C |
[0;6,1,3,2,5,1,6,5,3,1,1,2,1,1,2,3,1,2,3,2,2,...] |
|
0.14758361765043327417540107622474052 |
0.15915 49430 91895 33576[Mw 76] |
Plouffe's A constant[78] |
|
![{\displaystyle {A}}](//wikimedia.org/api/rest_v1/media/math/render/svg/f5ebb239b453149a6dedba8f18670ce9a9390c08) |
![{\displaystyle {\frac {1}{2\pi }}}](//wikimedia.org/api/rest_v1/media/math/render/svg/129204d50704b07e6a4223870954242b21170354) |
|
T |
ਫਰਮਾ:OEIS2C |
[0;6,3,1,1,7,2,146,3,6,1,1,2,7,5,5,1,4,1,2,42,...] |
|
0.15915494309189533576888376337251436 |
0.29156 09040 30818 78013[Mw 77] |
Dimer constant 2D, Domino tiling[79][80] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Dominoes_tiling_8x8.svg/100px-Dominoes_tiling_8x8.svg.png) |
C=Catalan |
![{\displaystyle \int \limits _{-\pi }^{\pi }{\frac {\cosh ^{-1}\left({\frac {\sqrt {\cos(t)+3}}{\sqrt {2}}}\right)}{4\pi }}\,dt}](//wikimedia.org/api/rest_v1/media/math/render/svg/07df19c41235e8c93b379a3f4b5e1a5d51a0cdef) |
N[int[-pi to pi]
{arccosh(sqrt(
cos(t)+3)/sqrt(2))
/(4*Pi)dt}]
|
|
ਫਰਮਾ:OEIS2C |
[0;3,2,3,16,8,10,3,1,1,2,1,3,1,2,13,1,1,4,1,5,...] |
|
0.29156090403081878013838445646839491 |
0.49801 56681 18356 04271
0.15494 98283 01810 68512 i |
Factorial(i)[81] |
|
![{\displaystyle {i}\,!}](//wikimedia.org/api/rest_v1/media/math/render/svg/759e437f1583d78b558ecf693c9e63c76edaa48e) |
![{\displaystyle \Gamma (1+i)=i\,\Gamma (i)=\int \limits _{0}^{\infty }{\frac {t^{i}}{e^{t}}}\mathrm {d} t}](//wikimedia.org/api/rest_v1/media/math/render/svg/610122cc74e86248f0d3534913db6865e57ba79b) |
|
C |
ਫਰਮਾ:OEIS2C ਫਰਮਾ:OEIS2C |
[0;6,2,4,1,8,1,46,2,2,3,5,1,10,7,5,1,7,2,...] - [0;2,125,2,18,1,2,1,1,19,1,1,1,2,3,34,...] i |
|
0.49801566811835604271369111746219809 - 0.15494982830181068512495513048388 i |
2.09455 14815 42326 59148[Mw 78] |
Wallis Constant |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Wallis%27s_Constant.png/100px-Wallis%27s_Constant.png) |
![{\displaystyle W}](//wikimedia.org/api/rest_v1/media/math/render/svg/54a9c4c547f4d6111f81946cad242b18298d70b7) |
![{\displaystyle {\sqrt[{3}]{\frac {45-{\sqrt {1929}}}{18}}}+{\sqrt[{3}]{\frac {45+{\sqrt {1929}}}{18}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/f4a477d1c213e6e2b9bad2f5190a12810278e06a) |
(((45-sqrt(1929))
/18))^(1/3)+
(((45+sqrt(1929))
/18))^(1/3)
|
A |
ਫਰਮਾ:OEIS2C |
[2;10,1,1,2,1,3,1,1,12,3,5,1,1,2,1,6,1,11,4,...] |
1616 to 1703 |
2.09455148154232659148238654057930296 |
0.72364 84022 98200 00940[Mw 79] |
Sarnak constant |
|
![{\displaystyle {C_{sa}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/81d78cc0244cf6e92cefa79c9b468817d2708d4f) |
![{\displaystyle \prod _{p>2}{\Big (}1-{\frac {p+2}{p^{3}}}{\Big )}}](//wikimedia.org/api/rest_v1/media/math/render/svg/bdcd4abcda6f3f229f3b39a47f9a56dd10ddb4ef) |
N[prod[k=2 to ∞]
{1-(prime(k)+2)
/(prime(k)^3)}]
|
T ? |
ਫਰਮਾ:OEIS2C |
[0;1,2,1,1,1,1,1,1,1,4,4,1,1,1,1,1,1,1,8,2,1,1,...] |
|
0.72364840229820000940884914980912759 |
0.63212 05588 28557 67840[Mw 80] |
Time constant[82] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Seq1.png/100px-Seq1.png) |
![{\displaystyle {\tau }}](//wikimedia.org/api/rest_v1/media/math/render/svg/8d2cbbb2bd6bed8835c6a57e58a152568e6f7fa8) |
![{\displaystyle \sum \limits _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n!}}={\frac {1}{1!}}{-}{\frac {1}{2!}}{+}{\frac {1}{3!}}{-}{\frac {1}{4!}}{+}{\frac {1}{5!}}{-}{\frac {1}{6!}}{+}\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/1e87627ba57f881e54c0371bc99f9fe5ec7a7907)
|
lim_(n->∞) (1- !n/n!)
!n=subfactorial
|
T |
ਫਰਮਾ:OEIS2C |
[0;1,1,1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1,...] = [0;1,1,1,2n], n∈ℕ |
|
0.63212055882855767840447622983853913 |
1.04633 50667 70503 18098 |
Minkowski-Siegel mass constant[83] |
|
![{\displaystyle F_{1}}](//wikimedia.org/api/rest_v1/media/math/render/svg/100c7fbf174fe8b06eacc2a6b0bb2e1badd1c7ce) |
![{\displaystyle \prod _{n=1}^{\infty }{\frac {n!}{{\sqrt {2\pi n}}\left({\frac {n}{e}}\right)^{n}{\sqrt[{12}]{1+{\tfrac {1}{n}}}}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/81ce7cd71c37a3c97c3b4244332953b626c26900) |
N[prod[n=1 to ∞]
n! /(sqrt(2*Pi*n)
*(n/e)^n *(1+1/n)
^(1/12))]
|
|
ਫਰਮਾ:OEIS2C |
[1;21,1,1,2,1,1,4,2,1,5,7,2,1,20,1,1,1134,3,..] |
1867 1885 1935 |
1.04633506677050318098095065697776037 |
5.24411 51085 84239 62092[Mw 81] |
Lemniscate Constant[84] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Lemniscate_of_Bernoulli.gif/80px-Lemniscate_of_Bernoulli.gif) |
![{\displaystyle 2\varpi }](//wikimedia.org/api/rest_v1/media/math/render/svg/fe51c6334f321b77d69548761bef169d47265a15) |
![{\displaystyle {\frac {[\Gamma ({\tfrac {1}{4}})]^{2}}{\sqrt {2\pi }}}=4\int _{0}^{1}{\frac {dx}{\sqrt {(1-x^{2})(2-x^{2})}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/838230a1a8781844335c2977f729a38f594a7da6) |
Gamma[ 1/4 ]^2
/Sqrt[ 2 Pi ]
|
|
ਫਰਮਾ:OEIS2C |
[5;4,10,2,1,2,3,29,4,1,2,1,2,1,2,1,4,9,1,4,1,2,...] |
1718 |
5.24411510858423962092967917978223883 |
0.66170 71822 67176 23515[Mw 82] |
Robbins constant[85] |
|
![{\displaystyle \Delta (3)}](//wikimedia.org/api/rest_v1/media/math/render/svg/d6d496e74dd3b8183678a63b064775599e485aa0) |
![{\displaystyle {\frac {4\!+\!17{\sqrt {2}}\!-6{\sqrt {3}}\!-7\pi }{105}}\!+\!{\frac {\ln(1\!+\!{\sqrt {2}})}{5}}\!+\!{\frac {2\ln(2\!+\!{\sqrt {3}})}{5}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/4d4f22a74d02f2635c0bba2278995dfc6eabb11f) |
(4+17*2^(1/2)-6
*3^(1/2)+21*ln(1+
2^(1/2))+42*ln(2+
3^(1/2))-7*Pi)/105
|
|
ਫਰਮਾ:OEIS2C |
[0;1,1,1,21,1,2,1,4,10,1,2,2,1,3,11,1,331,1,4,...] |
1978 |
0.66170718226717623515583113324841358 |
1.30357 72690 34296 39125[Mw 83] |
Conway constant[86] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Conway_constant.png/100px-Conway_constant.png) |
![{\displaystyle {\lambda }}](//wikimedia.org/api/rest_v1/media/math/render/svg/80912e657954ba7a08dc822fac02fd5fd61067c1) |
![{\displaystyle {\begin{smallmatrix}x^{71}\quad \ -x^{69}-2x^{68}-x^{67}+2x^{66}+2x^{65}+x^{64}-x^{63}-x^{62}-x^{61}-x^{60}\\-x^{59}+2x^{58}+5x^{57}+3x^{56}-2x^{55}-10x^{54}-3x^{53}-2x^{52}+6x^{51}+6x^{50}\\+x^{49}+9x^{48}-3x^{47}-7x^{46}-8x^{45}-8x^{44}+10x^{43}+6x^{42}+8x^{41}-5x^{40}\\-12x^{39}+7x^{38}-7x^{37}+7x^{36}+x^{35}-3x^{34}+10x^{33}+x^{32}-6x^{31}-2x^{30}\\-10x^{29}-3x^{28}+2x^{27}+9x^{26}-3x^{25}+14x^{24}-8x^{23}\quad \ -7x^{21}+9x^{20}\\+3x^{19}\!-4x^{18}\!-10x^{17}\!-7x^{16}\!+12x^{15}\!+7x^{14}\!+2x^{13}\!-12x^{12}\!-4x^{11}\!-2x^{10}\\+5x^{9}+x^{7}\quad \ -7x^{6}+7x^{5}-4x^{4}+12x^{3}-6x^{2}+3x-6\ =\ 0\quad \quad \quad \end{smallmatrix}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/ceb783dfe6c5c82e3a566c2bb2d59cd9d6a145f6) |
|
A |
ਫਰਮਾ:OEIS2C |
[1;3,3,2,2,54,5,2,1,16,1,30,1,1,1,2,2,1,14,1,...] |
1987 |
1.30357726903429639125709911215255189 |
1.18656 91104 15625 45282[Mw 84] |
Khinchin–Lévy constant[87] |
|
![{\displaystyle {\beta }}](//wikimedia.org/api/rest_v1/media/math/render/svg/4f08e5bb6adcac8ac464df79e6a2e43779898ab7) |
![{\displaystyle {\frac {\pi ^{2}}{12\,\ln 2}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/b7c204d987401c9c008ff2e986391871ba85f64f) |
|
|
ਫਰਮਾ:OEIS2C |
[1;5,2,1,3,1,1,28,18,16,3,2,6,2,6,1,1,5,5,9,...] |
1935 |
1.18656911041562545282172297594723712 |
0.83564 88482 64721 05333 |
Baker constant[88] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Baker_constant.png/100px-Baker_constant.png) |
![{\displaystyle \beta _{3}}](//wikimedia.org/api/rest_v1/media/math/render/svg/5b1001bcd6968314a965726f5dd193d1b11ada59) |
![{\displaystyle \int _{0}^{1}{\frac {\mathrm {d} t}{1+t^{3}}}=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{3n+1}}={\frac {1}{3}}\left(\ln 2+{\frac {\pi }{\sqrt {3}}}\right)}](//wikimedia.org/api/rest_v1/media/math/render/svg/163cba30d04a96de40f0bc025bf3d2ff2c141fd1) |
Sum[n=0 to ∞]
{((-1)^(n))/(3n+1)}
|
|
ਫਰਮਾ:OEIS2C |
[0;1,5,11,1,4,1,6,1,4,1,1,1,2,1,3,2,2,2,2,1,3,...] |
|
0.83564884826472105333710345970011076 |
23.10344 79094 20541 6160[Mw 85] |
Kempner Serie(0)[89] |
|
![{\displaystyle {K_{0}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/bca8f32a2230a34edb8aee88f5fbf1d4cc9e2d67) |
![{\displaystyle {+}{\frac {1}{99}}{+}{\frac {1}{111}}{+}\cdots {+}{\frac {1}{119}}{+}{\frac {1}{121}}{+}\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/fe9c152608344a586c34d1ec4edfbcc967d9cf96)
(Excluding all denominators containing 0.) |
1+1/2+1/3+1/4+1/5
+1/6+1/7+1/8+1/9
+1/11+1/12+1/13
+1/14+1/15+...
|
|
ਫਰਮਾ:OEIS2C |
[23;9,1,2,3244,1,1,5,1,2,2,8,3,1,1,6,1,84,1,...] |
|
23.1034479094205416160340540433255981 |
0.98943 12738 31146 95174[Mw 86] |
Lebesgue constant[90] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Fourier_synthesis.svg/100px-Fourier_synthesis.svg.png) |
![{\displaystyle {C_{1}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/f15c9f7a08b112a63a9edf64f9c6e3c959820326) |
![{\displaystyle \lim _{n\to \infty }\!\!\left(\!{L_{n}{-}{\frac {4}{\pi ^{2}}}\ln(2n{+}1)}\!\!\right)\!{=}{\frac {4}{\pi ^{2}}}\!\left({\sum _{k=1}^{\infty }\!{\frac {2\ln k}{4k^{2}{-}1}}}{-}{\frac {\Gamma '({\tfrac {1}{2}})}{\Gamma ({\tfrac {1}{2}})}}\!\!\right)}](//wikimedia.org/api/rest_v1/media/math/render/svg/d386c483388c4caa0b0900e5dc90d8349e29a67a) |
4/pi^2*[(2
Sum[k=1 to ∞]
{ln(k)/(4*k^2-1)})
-poligamma(1/2)]
|
|
ਫਰਮਾ:OEIS2C |
[0;1,93,1,1,1,1,1,1,1,7,1,12,2,15,1,2,7,2,1,5,...] |
? |
0.98943127383114695174164880901886671 |
0.19452 80494 65325 11361[Mw 87] |
2nd du Bois-Reymond constant[91] |
|
![{\displaystyle {C_{2}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/58b8a880a028faf6c40eca9385b90538f3ee8d77) |
![{\displaystyle {\frac {e^{2}-7}{2}}=\int _{0}^{\infty }\left|{{\frac {d}{dt}}\left({\frac {\sin t}{t}}\right)^{n}}\right|\,dt-1}](//wikimedia.org/api/rest_v1/media/math/render/svg/e2e6ba3643eb29411387cd701f50b3ee1fbbe4df) |
|
T |
ਫਰਮਾ:OEIS2C |
[0;5,7,9,11,13,15,17,19,21,23,25,27,29,31,...] = [0;2p+3], p∈ℕ |
|
0.19452804946532511361521373028750390 |
0.78853 05659 11508 96106[Mw 88] |
Lüroth constant[92] |
![](//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Constante_de_L%C3%BCroth.svg/35px-Constante_de_L%C3%BCroth.svg.png) |
![{\displaystyle C_{L}}](//wikimedia.org/api/rest_v1/media/math/render/svg/6bd8f93b1f511b05ced33ab7fcfceab8072cdb01) |
![{\displaystyle \sum _{n=2}^{\infty }{\frac {\ln \left({\frac {n}{n-1}}\right)}{n}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/52cd10bab6c89827c10fa228a743e322aa59bd0c) |
Sum[n=2 to ∞]
log(n/(n-1))/n
|
|
ਫਰਮਾ:OEIS2C |
[0;1,3,1,2,1,2,4,1,127,1,2,2,1,3,8,1,1,2,1,16,...] |
|
0.78853056591150896106027632216944432 |
1.18745 23511 26501 05459[Mw 89] |
Foias constant α[93] |
|
![{\displaystyle F_{\alpha }}](//wikimedia.org/api/rest_v1/media/math/render/svg/f398142fc1e8e07fddf8f1b8705e6bcb3473398d) |
Foias constant is the unique real number such that if x1 = α then the sequence diverges to ∞. When x1 = α, ![{\displaystyle \,\lim _{n\to \infty }x_{n}{\tfrac {\log n}{n}}=1}](//wikimedia.org/api/rest_v1/media/math/render/svg/034350030587639b181e410dbb19cf896e1b48a3) |
|
|
ਫਰਮਾ:OEIS2C |
[1;5,2,1,81,3,2,2,1,1,1,1,1,6,1,1,3,1,1,4,3,2,...] |
2000 |
1.18745235112650105459548015839651935 |
2.29316 62874 11861 03150[Mw 90] |
Foias constant β |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Foias_constant.png/100px-Foias_constant.png) |
![{\displaystyle F_{\beta }}](//wikimedia.org/api/rest_v1/media/math/render/svg/eb39f5958eb83bc3c28cd8b1a5397d3bb14fecdf) |
![{\displaystyle x^{x+1}=(x+1)^{x}}](//wikimedia.org/api/rest_v1/media/math/render/svg/fc0e6d310dd8f48cd472af63e12a68951102d779) |
|
|
ਫਰਮਾ:OEIS2C |
[2;3,2,2,3,4,2,3,2,130,1,1,1,1,1,6,3,2,1,15,1,...] |
2000 |
2.29316628741186103150802829125080586 |
0.82246 70334 24113 21823[Mw 91] |
Nielsen-Ramanujan constant[94] |
|
![{\displaystyle {\frac {{\zeta }(2)}{2}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/dcea6028ed307f4f120f5092408c8d2c2063ada1) |
![{\displaystyle {\frac {\pi ^{2}}{12}}=\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{n^{2}}}={\frac {1}{1^{2}}}{-}{\frac {1}{2^{2}}}{+}{\frac {1}{3^{2}}}{-}{\frac {1}{4^{2}}}{+}{\frac {1}{5^{2}}}{-}\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/8b55d24a84171680659cd9b88940404b78b304a6) |
Sum[n=1 to ∞]
{((-1)^(n+1))/n^2}
|
T |
ਫਰਮਾ:OEIS2C |
[0;1,4,1,1,1,2,1,1,1,1,3,2,2,4,1,1,1,1,1,1,4...] |
1909 |
0.82246703342411321823620758332301259
|
0.69314 71805 59945 30941[Mw 92] |
Natural logarithm of 2[95] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/0/08/Alternating_Harmonic_Series.PNG/100px-Alternating_Harmonic_Series.PNG) |
![{\displaystyle Ln(2)}](//wikimedia.org/api/rest_v1/media/math/render/svg/bb83d89d81f592ea17f250befb3a6ed523c80122) |
![{\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n2^{n}}}=\sum _{n=1}^{\infty }{\frac {({-}1)^{n+1}}{n}}={\frac {1}{1}}-{\frac {1}{2}}+{\frac {1}{3}}-{\frac {1}{4}}+{\cdots }}](//wikimedia.org/api/rest_v1/media/math/render/svg/9fb47b91c76d601161e8704cd72ade3d4d4d1d58) |
Sum[n=1 to ∞]
{(-1)^(n+1)/n}
|
T |
ਫਰਮਾ:OEIS2C |
[0;1,2,3,1,6,3,1,1,2,1,1,1,1,3,10,1,1,1,2,1,1,...] |
1550 to 1617 |
0.69314718055994530941723212145817657 |
0.47494 93799 87920 65033[Mw 93] |
Weierstrass constant[96] |
|
![{\displaystyle \sigma ({\tfrac {1}{2}})}](//wikimedia.org/api/rest_v1/media/math/render/svg/1fe4199f43a0e8cf205634ef6e9e61fd3386ab50) |
![{\displaystyle {\frac {e^{\frac {\pi }{8}}{\sqrt {\pi }}}{4\cdot 2^{3/4}{({\frac {1}{4}}!)^{2}}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/202077dafb40266a18a7290ff112e736368fd440) |
(E^(Pi/8) Sqrt[Pi])
/(4 2^(3/4) (1/4)!^2)
|
|
ਫਰਮਾ:OEIS2C |
[0;2,9,2,11,1,6,1,4,6,3,19,9,217,1,2,4,8,6...] |
1872 ? |
0.47494937998792065033250463632798297 |
0.57721 56649 01532 86060[Mw 94] |
Euler–Mascheroni constant |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Euler-Mas.jpg/100px-Euler-Mas.jpg) |
![{\displaystyle {\gamma }}](//wikimedia.org/api/rest_v1/media/math/render/svg/0c5a51bb731eb471125cf853d8c845695870617f) |
![{\displaystyle =\int _{0}^{1}-\ln \left(\ln {\frac {1}{x}}\right)\,dx=-\Gamma '(1)=-\Psi (1)}](//wikimedia.org/api/rest_v1/media/math/render/svg/518908bd133462dd5c19c00408536d5e9cfb934e)
|
sum[n=1 to ∞]
|sum[k=0 to ∞]
{((-1)^k)/(2^n+k)}
|
|
ਫਰਮਾ:OEIS2C |
[0;1,1,2,1,2,1,4,3,13,5,1,1,8,1,2,4,1,1,40,1,...] |
1735 |
0.57721566490153286060651209008240243
|
1.38135 64445 18497 79337 |
Beta, Kneser-Mahler polynomial constant[97] |
|
![{\displaystyle \beta }](//wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8) |
![{\displaystyle e^{^{\textstyle {\frac {2}{\pi }}\displaystyle {\int _{0}^{\frac {\pi }{3}}}\textstyle {t\tan t\ dt}}}=e^{^{\displaystyle {\,\int _{\frac {-1}{3}}^{\frac {1}{3}}}\textstyle {\,\ln \lfloor 1+e^{2\pi it}}\rfloor dt}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/c0e0546f793fb7ace2f4fdc23dd4159ce80b7f50) |
e^((PolyGamma(1,4/3)
- PolyGamma(1,2/3)
+9)/(4*sqrt(3)*Pi))
|
|
ਫਰਮਾ:OEIS2C |
[1;2,1,1,1,1,1,4,1,139,2,1,3,5,16,2,1,1,7,2,1,...] |
1963 |
1.38135644451849779337146695685062412 |
1.35845 62741 82988 43520[Mw 95] |
Golden Spiral |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/FakeRealLogSpiral.svg/100px-FakeRealLogSpiral.svg.png) |
![{\displaystyle c}](//wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455) |
![{\displaystyle \varphi ^{\frac {2}{\pi }}=\left({\frac {1+{\sqrt {5}}}{2}}\right)^{\frac {2}{\pi }}}](//wikimedia.org/api/rest_v1/media/math/render/svg/c26378c3209eb358366c3768bf456258d4a9fd2e) |
|
|
ਫਰਮਾ:OEIS2C |
[1;2,1,3,1,3,10,8,1,1,8,1,15,6,1,3,1,1,2,3,1,1,...] |
|
1.35845627418298843520618060050187945
|
0.57595 99688 92945 43964[Mw 96] |
Stephens constant[98] |
|
![{\displaystyle C_{S}}](//wikimedia.org/api/rest_v1/media/math/render/svg/4756cefa16309fd1faefd2d831257cd74868705c) |
![{\displaystyle \prod _{n=1}^{\infty }\left(1-{\frac {p}{p^{3}-1}}\right)}](//wikimedia.org/api/rest_v1/media/math/render/svg/a96860498271875e609a147f8c4fc6020b5db4e8) |
Prod[n=1 to ∞]
{1-hprime(n)
/(hprime(n)^3-1)}
|
T ? |
ਫਰਮਾ:OEIS2C |
[0;1,1,2,1,3,1,3,1,2,1,77,2,1,1,10,2,1,1,1,7,...] |
? |
0.57595996889294543964316337549249669 |
0.73908 51332 15160 64165[Mw 97] |
Dottie number[99] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Dottie_number.png/100px-Dottie_number.png) |
![{\displaystyle d}](//wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab) |
![{\displaystyle \lim _{x\to \infty }\cos ^{[x]}(c)=\lim _{x\to \infty }\underbrace {\cos(\cos(\cos(\cdots (\cos(c)))))} _{x}}](//wikimedia.org/api/rest_v1/media/math/render/svg/6289b54ab365ac6378e5e9511f7cbea085bdace9) |
|
T |
ਫਰਮਾ:OEIS2C |
[0;1,2,1,4,1,40,1,9,4,2,1,15,2,12,1,21,1,17,...] |
? |
0.73908513321516064165531208767387340 |
0.67823 44919 17391 97803[Mw 98] |
Taniguchi constant[100] |
|
![{\displaystyle C_{T}}](//wikimedia.org/api/rest_v1/media/math/render/svg/f6003ca59bfce8f624dd45e8ee023d098c7923cb) |
![{\displaystyle \scriptstyle p_{n}=\,{\text{prime}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/d65b22a26a250ba1ef31e6103c77411e67d0f52a) |
Prod[n=1 to ∞] {1
-3/ithprime(n)^3
+2/ithprime(n)^4
+1/ithprime(n)^5
-1/ithprime(n)^6}
|
T ? |
ਫਰਮਾ:OEIS2C |
[0;1,2,9,3,1,2,9,11,1,13,2,15,1,1,1,2,4,1,1,1,...] |
? |
0.67823449191739197803553827948289481 |
1.85407 46773 01371 91843[Mw 99] |
Gauss' Lemniscate constant[101] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Lemniscate_Building.gif/100px-Lemniscate_Building.gif) |
![{\displaystyle L{\text{/}}{\sqrt {2}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/b7a4961d05494b3f911bfdf72227f87e7f01a589) |
![{\displaystyle \scriptstyle \Gamma (){\text{= Gamma function}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/c9988848b7807dcf9695eaa182b31760c5462967) |
pi^(3/2)/(2 Gamma(3/4)^2)
|
|
ਫਰਮਾ:OEIS2C |
[1;1,5,1,5,1,3,1,6,2,1,4,16,3,112,2,1,1,18,1,...] |
|
1.85407467730137191843385034719526005 |
1.75874 36279 51184 82469 |
Infinite product constant, with Alladi-Grinstead[102] |
|
![{\displaystyle Pr_{1}}](//wikimedia.org/api/rest_v1/media/math/render/svg/2d7e20f2999fc5052964285a74a0b20ce21fa0fd) |
![{\displaystyle \prod _{n=2}^{\infty }{\Big (}1+{\frac {1}{n}}{\Big )}^{\frac {1}{n}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/d814a4959a4e92a9e45faf20baf323d4680a8846) |
Prod[n=2 to inf]
{(1+1/n)^(1/n)}
|
|
ਫਰਮਾ:OEIS2C |
[1;1,3,6,1,8,1,4,3,1,4,1,1,1,6,5,2,40,1,387,2,...] |
1977 |
1.75874362795118482469989684865589317 |
1.86002 50792 21190 30718 |
Spiral of Theodorus[103] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Spiral_of_Theodorus.svg/100px-Spiral_of_Theodorus.svg.png) |
![{\displaystyle \partial }](//wikimedia.org/api/rest_v1/media/math/render/svg/62b4e7c1cedb9564609aefd2aa2309972f455c24) |
![{\displaystyle \sum _{n=1}^{\infty }{\frac {1}{{\sqrt {n^{3}}}+{\sqrt {n}}}}=\sum _{n=1}^{\infty }{\frac {1}{{\sqrt {n}}(n+1)}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/10543d0b7e354ae16f280cf80da47209270a29bb) |
Sum[n=1 to ∞]
{1/(n^(3/2)
+n^(1/2))}
|
|
ਫਰਮਾ:OEIS2C |
[1;1,6,6,1,15,11,5,1,1,1,1,5,3,3,3,2,1,1,2,19,...] |
-460 to -399 |
1.86002507922119030718069591571714332 |
2.79128 78474 77920 00329 |
Nested radical S5 |
|
![{\displaystyle S_{5}}](//wikimedia.org/api/rest_v1/media/math/render/svg/7d113353a42f71fc5e7154ddef2257079ab2e25a) |
![{\displaystyle =1+\,\scriptstyle {\sqrt {5-{\sqrt {5-{\sqrt {5-{\sqrt {5-{\sqrt {5-\cdots }}}}}}}}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/aa58c3189f25c5f253b654f82009ef8fd2a8d384)
|
|
A |
A222134 |
[2;1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,...] [2;1,3] |
? |
2.79128784747792000329402359686400424 |
0.70710 67811 86547 52440 +0.70710 67811 86547 524 i[Mw 100] |
Square root of i[104] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Imaginary2Root.svg/100px-Imaginary2Root.svg.png) |
![{\displaystyle {\sqrt {i}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/5673f4281fbb14875cb48ddd2ddbcc1aa63ab8dd) |
![{\displaystyle {\sqrt[{4}]{-1}}={\frac {1+i}{\sqrt {2}}}=e^{\frac {i\pi }{4}}=\cos \left({\frac {\pi }{4}}\right)+i\sin \left({\frac {\pi }{4}}\right)}](//wikimedia.org/api/rest_v1/media/math/render/svg/37c0f3410cad402cfea4cf785416d99e3b2f417d) |
|
C A |
ਫਰਮਾ:OEIS2C |
[0;1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,..] = [0;1,2,...] [0;1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,..] i = [0;1,2,...] i |
? |
0.70710678118654752440084436210484903 + 0.70710678118654752440084436210484 i |
0.80939 40205 40639 13071[Mw 101] |
Alladi–Grinstead constant[105] |
|
![{\displaystyle {{\mathcal {A}}_{AG}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/c06e9ce995c4020365ec0e144956ae72927ef683) |
![{\displaystyle e^{-1+\sum \limits _{k=2}^{\infty }\sum \limits _{n=1}^{\infty }{\frac {1}{nk^{n+1}}}}=e^{-1-\sum \limits _{k=2}^{\infty }{\frac {1}{k}}\ln \left(1-{\frac {1}{k}}\right)}}](//wikimedia.org/api/rest_v1/media/math/render/svg/e003dc6c33634375498de4709443e201e917f11d) |
e^{(sum[k=2 to ∞]
|sum[n=1 to ∞]
{1/(n k^(n+1))})-1}
|
|
ਫਰਮਾ:OEIS2C |
[0;1,4,4,17,4,3,2,5,3,1,1,1,1,6,1,1,2,1,22,...] |
1977 |
0.80939402054063913071793188059409131 |
2.58498 17595 79253 21706[Mw 102] |
Sierpiński's constant[106] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Random_Sierpinski_Triangle_animation.gif/100px-Random_Sierpinski_Triangle_animation.gif) |
![{\displaystyle {K}}](//wikimedia.org/api/rest_v1/media/math/render/svg/58e8935f16888d2f0621f2c4f3021469dcef9e3d) |
![{\displaystyle =\pi \left(2\ln 2+3\ln \pi +2\gamma -4\ln \Gamma ({\tfrac {1}{4}})\right)}](//wikimedia.org/api/rest_v1/media/math/render/svg/f23184c1373d37053b1653000d23ea60b9508e6f)
|
-Pi Log[Pi]+2 Pi
EulerGamma
+4 Pi Log
[Gamma[3/4]]
|
|
ਫਰਮਾ:OEIS2C |
[2;1,1,2,2,3,1,3,1,9,2,8,4,1,13,3,1,15,18,1,...] |
1907 |
2.58498175957925321706589358738317116 |
1.73245 47146 00633 47358[Ow 4] |
Reciprocal of the Euler–Mascheroni constant |
|
![{\displaystyle {\frac {1}{\gamma }}}](//wikimedia.org/api/rest_v1/media/math/render/svg/b213c1cb55c916bee395d544e1b5a75fddc6a0ef) |
![{\displaystyle \left(\int _{0}^{1}-\log \left(\log {\frac {1}{x}}\right)\,dx\right)^{-1}=\sum _{n=1}^{\infty }(-1)^{n}(-1+\gamma )^{n}}](//wikimedia.org/api/rest_v1/media/math/render/svg/8f7cdc3bdb40d4037b76f6cb504d85c548cdb83a) |
1/Integrate_
{x=0 to 1}
-log(log(1/x))
|
|
ਫਰਮਾ:OEIS2C |
[1;1,2,1,2,1,4,3,13,5,1,1,8,1,2,4,1,1,40,1,11,...] |
|
1.73245471460063347358302531586082968 |
1.43599 11241 76917 43235[Mw 103] |
Lebesgue constant (interpolation)[107][108] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Fourier_series_integral_identities.gif/100px-Fourier_series_integral_identities.gif) |
![{\displaystyle {L_{1}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/a355a82649e4b1533d47851a28b42b6e0d74ff1b) |
![{\displaystyle \prod _{\begin{smallmatrix}i=0\\j\neq i\end{smallmatrix}}^{n}{\frac {x-x_{i}}{x_{j}-x_{i}}}={\frac {1}{\pi }}\int _{0}^{\pi }{\frac {\lfloor \sin {\frac {3t}{2}}\rfloor }{\sin {\frac {t}{2}}}}\,dt={\frac {1}{3}}+{\frac {2{\sqrt {3}}}{\pi }}}](//wikimedia.org/api/rest_v1/media/math/render/svg/8efee14ec97811fe40fffea481ed59d623b139cc) |
|
T |
ਫਰਮਾ:OEIS2C |
[1;2,3,2,2,6,1,1,1,1,4,1,7,1,1,1,2,1,3,1,2,1,1,...] |
1902 ~ |
1.43599112417691743235598632995927221 |
3.24697 96037 17467 06105[Mw 104] |
Silver root Tutte–Beraha constant[109] |
|
![{\displaystyle \varsigma }](//wikimedia.org/api/rest_v1/media/math/render/svg/5d1fab64d12c6ee8fbf378b73072d0cf13c8c4f7) |
![{\displaystyle 2+2\cos {\frac {2\pi }{7}}=\textstyle 2+{\frac {2+{\sqrt[{3}]{7+7{\sqrt[{3}]{7+7{\sqrt[{3}]{\,7+\cdots }}}}}}}{1+{\sqrt[{3}]{7+7{\sqrt[{3}]{7+7{\sqrt[{3}]{\,7+\cdots }}}}}}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/df4b6dfb762686eef1476628b27712ce19606c54) |
|
A |
ਫਰਮਾ:OEIS2C |
[3;4,20,2,3,1,6,10,5,2,2,1,2,2,1,18,1,1,3,2,...] |
|
3.24697960371746706105000976800847962 |
1.94359 64368 20759 20505[Mw 105] |
Euler Totient constant[110][111] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/EulerPhi100.svg/100px-EulerPhi100.svg.png) |
![{\displaystyle ET}](//wikimedia.org/api/rest_v1/media/math/render/svg/1de0ba313205b0abbc915b3d313bc01cfc97a4fc) |
![{\displaystyle {\underset {p{\text{= primes}}}{\prod _{p}{\Big (}1+{\frac {1}{p(p-1)}}{\Big )}}}={\frac {\zeta (2)\zeta (3)}{\zeta (6)}}={\frac {315\zeta (3)}{2\pi ^{4}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/308ef1aad9ebd584b96199b2a8f56a690adb0a37) |
|
|
ਫਰਮਾ:OEIS2C |
[1;1,16,1,2,1,2,3,1,1,3,2,1,8,1,1,1,1,1,1,1,32,...] |
1750 |
1.94359643682075920505707036257476343 |
1.49534 87812 21220 54191 |
Fourth root of five[112] |
|
![{\displaystyle {\sqrt[{4}]{5}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/5ca317d0c75e7b6f908151e893d8a05f990ee060) |
![{\displaystyle {\sqrt[{5}]{5\,{\sqrt[{5}]{5\,{\sqrt[{5}]{5\,{\sqrt[{5}]{5\,{\sqrt[{5}]{5\,\cdots }}}}}}}}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/3127d3db98c6e81870992019a1d56264a39f7a90) |
(5(5(5(5(5(5(5)
^1/5)^1/5)^1/5)
^1/5)^1/5)^1/5)
^1/5 ...
|
A |
ਫਰਮਾ:OEIS2C |
[1;2,53,4,96,2,1,6,2,2,2,6,1,4,1,49,17,2,3,2,...] |
|
1.49534878122122054191189899414091339 |
0.87228 40410 65627 97617[Mw 106] |
Area of Ford circle[113] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Circumfer%C3%A8ncies_de_Ford.svg/100px-Circumfer%C3%A8ncies_de_Ford.svg.png) |
![{\displaystyle A_{CF}}](//wikimedia.org/api/rest_v1/media/math/render/svg/e837f8b3f2f9bf14efd27bfdbe3ae24a5040c473) |
![{\displaystyle \sum _{q\geq 1}\sum _{(p,q)=1 \atop 1\leq p<q}\pi \left({\frac {1}{2q^{2}}}\right)^{2}{\underset {\zeta (){\text{= Riemann Zeta Function}}}{={\frac {\pi }{4}}{\frac {\zeta (3)}{\zeta (4)}}={\frac {45}{2}}{\frac {\zeta (3)}{\pi ^{3}}}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/285ec4ed03551cae9b1b0b2e11e083877b3c43a4) |
|
|
|
[0;1,6,1,4,1,7,5,36,3,29,1,1,10,3,2,8,1,1,1,3,...] |
|
0.87228404106562797617519753217122587 |
1.08232 32337 11138 19151[Mw 107] |
Zeta(4)[114] |
|
![{\displaystyle \zeta (4)}](//wikimedia.org/api/rest_v1/media/math/render/svg/9fd0a1bd6700d2dd56b5dad6f817674fdfd1ae43) |
![{\displaystyle {\frac {\pi ^{4}}{90}}=\sum _{n=1}^{\infty }{\frac {1}{n^{4}}}={\frac {1}{1^{4}}}+{\frac {1}{2^{4}}}+{\frac {1}{3^{4}}}+{\frac {1}{4^{4}}}+{\frac {1}{5^{4}}}+...}](//wikimedia.org/api/rest_v1/media/math/render/svg/132cb9801d177dff58660469d83b2800e0ea3833) |
|
T |
ਫਰਮਾ:OEIS2C |
[1;12,6,1,3,1,4,183,1,1,2,1,3,1,1,5,4,2,7,23,...] |
? |
1.08232323371113819151600369654116790 |
1.56155 28128 08830 27491
|
Triangular root of 2.[115] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/3/33/N%C3%BAmeros_triangulares.png/100px-N%C3%BAmeros_triangulares.png) |
![{\displaystyle {R_{2}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/1547957bdd650785de8bba197fc2aa01f4690ac4) |
![{\displaystyle =\,\scriptstyle {\sqrt {4-{\sqrt {4-{\sqrt {4-{\sqrt {4-{\sqrt {4-{\sqrt {4-\cdots }}}}}}}}}}}}\textstyle }](//wikimedia.org/api/rest_v1/media/math/render/svg/491f18afcc7e3c29c7d47d42ea2ed7cb0cebbdd0)
|
|
A |
ਫਰਮਾ:OEIS2C |
[1;1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1,...] [1;1,1,3] |
|
1.56155281280883027491070492798703851 |
9.86960 44010 89358 61883 |
Pi Squared |
|
![{\displaystyle {\pi }^{2}}](//wikimedia.org/api/rest_v1/media/math/render/svg/4687b7b6e9fce272a1858ca9107e3c74a8679bfc) |
![{\displaystyle 6\,\zeta (2)=6\sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {6}{1^{2}}}+{\frac {6}{2^{2}}}+{\frac {6}{3^{2}}}+{\frac {6}{4^{2}}}+\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/b379c6dc4e57554c90186d08ae45c028d20e67fb) |
|
T |
A002388 |
[9;1,6,1,2,47,1,8,1,1,2,2,1,1,8,3,1,10,5,1,3,...] |
|
9.86960440108935861883449099987615114 |
1.32471 79572 44746 02596[Mw 108] |
Plastic number[116] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Nombre_plastique.svg/100px-Nombre_plastique.svg.png) |
![{\displaystyle {\rho }}](//wikimedia.org/api/rest_v1/media/math/render/svg/64fb820236ade4de4867d2ed7a0ff90ba32a5c6f) |
![{\displaystyle {\sqrt[{3}]{1+\!{\sqrt[{3}]{1+\!{\sqrt[{3}]{1+\cdots }}}}}}=\textstyle {\sqrt[{3}]{{\frac {1}{2}}+\!{\sqrt {\frac {23}{108}}}}}+\!{\sqrt[{3}]{{\frac {1}{2}}-\!{\sqrt {\frac {23}{108}}}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/d3e12d1e4a19b20855a66613f933081096edf018) |
(1+(1+(1+(1+(1+(1)
^(1/3))^(1/3))^(1/3))
^(1/3))^(1/3))^(1/3)
|
A |
ਫਰਮਾ:OEIS2C |
[1;3,12,1,1,3,2,3,2,4,2,141,80,2,5,1,2,8,2,...] |
1929 |
1.32471795724474602596090885447809734 |
2.37313 82208 31250 90564 |
Lévy 2 constant[117] |
|
![{\displaystyle 2\,ln\,\gamma }](//wikimedia.org/api/rest_v1/media/math/render/svg/ddf1fa571d43ba762e95f88e32948f40989bfde6) |
![{\displaystyle {\frac {\pi ^{2}}{6ln(2)}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/a1cc72ae43cd6716b31c625734d5660bc05c0661) |
|
T |
ਫਰਮਾ:OEIS2C |
[2;2,1,2,8,57,9,32,1,1,2,1,2,1,2,1,2,1,3,2,...] |
1936 |
2.37313822083125090564344595189447424 |
0.85073 61882 01867 26036[Mw 109] |
Regular paperfolding sequence[118][119] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Miura-ori.gif/100px-Miura-ori.gif) |
![{\displaystyle {P_{f}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/82d7a4ef9cbfa8020bad3ef7881883450927ce86) |
![{\displaystyle \sum _{n=0}^{\infty }{\frac {8^{2^{n}}}{2^{2^{n+2}}-1}}=\sum _{n=0}^{\infty }{\cfrac {\tfrac {1}{2^{2^{n}}}}{1-{\tfrac {1}{2^{2^{n+2}}}}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/741e2056cbedd4353f72cafb336dd7c402acc986) |
N[Sum[n=0 to ∞]
{8^2^n/(2^2^
(n+2)-1)},37]
|
|
ਫਰਮਾ:OEIS2C |
[0;1,5,1,2,3,21,1,4,107,7,5,2,1,2,1,1,2,1,6,...] |
|
0.85073618820186726036779776053206660 |
1.15636 26843 32269 71685[Mw 110] |
Cubic recurrence constant[120]{{.}}[121] |
|
![{\displaystyle {\sigma _{3}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/429dbbdb6aa4e994c4cc5a35445018372504d279) |
![{\displaystyle \prod _{n=1}^{\infty }n^{{3}^{-n}}={\sqrt[{3}]{1{\sqrt[{3}]{2{\sqrt[{3}]{3\cdots }}}}}}=1^{1/3}\;2^{1/9}\;3^{1/27}\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/d9e06c4b0df773f89d608077c7e00b4356a59994) |
prod[n=1 to ∞]
{n ^(1/3)^n}
|
|
ਫਰਮਾ:OEIS2C |
[1;6,2,1,1,8,13,1,3,2,2,6,2,1,2,1,1,1,10,33,...] |
|
1.15636268433226971685337032288736935 |
1.26185 95071 42914 87419[Mw 111] |
Fractal dimension of the Koch snowflake[122] |
|
![{\displaystyle {C_{k}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/63d4aca9774063d7181bafdecca68e960baed978) |
![{\displaystyle {\frac {\log 4}{\log 3}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/f5d139470ac298d1109209e1307eee3a664e8d62) |
|
T |
A100831 |
[1;3,1,4,1,1,11,1,46,1,5,112,1,1,1,1,1,3,1,7,...] |
|
1.26185950714291487419905422868552171 |
6.58088 59910 17920 97085 |
Froda constant[123] |
|
![{\displaystyle 2^{\,e}}](//wikimedia.org/api/rest_v1/media/math/render/svg/8bf33d4e76c5569823f25956ac3f30e423e41641) |
![{\displaystyle 2^{e}}](//wikimedia.org/api/rest_v1/media/math/render/svg/f2b0aea37d1c2c7e2cd2bd7bca87358232ed095c) |
|
|
|
[6;1,1,2,1,1,2,3,1,14,11,4,3,1,1,7,5,5,2,7,...] |
|
6.58088599101792097085154240388648649 |
0.26149 72128 47642 78375[Mw 112] |
Meissel-Mertens constant[124] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/a/ab/Meissel%E2%80%93Mertens_constant_definition.svg/100px-Meissel%E2%80%93Mertens_constant_definition.svg.png) |
![{\displaystyle {M}}](//wikimedia.org/api/rest_v1/media/math/render/svg/3e3134f64e8796a8f36cdfa1f70058c9cc484d8b) |
:\,{\text{Euler constant}},\,\,p:\,{\text{prime}}}{\!\gamma \!+\!\!\sum _{p}\!\left(\!\ln \!\left(\!1\!-\!{\frac {1}{p}}\!\right)\!\!+\!{\frac {1}{p}}\!\right)}}}
![{\displaystyle \lim _{n\rightarrow \infty }\!\!\left(\sum _{p\leq n}{\frac {1}{p}}\!-\ln(\ln(n))\!\right)\!\!={\underset {\!\!\!\!\gamma :\,{\text{Euler constant}},\,\,p:\,{\text{prime}}}{\!\gamma \!+\!\!\sum _{p}\!\left(\!\ln \!\left(\!1\!-\!{\frac {1}{p}}\!\right)\!\!+\!{\frac {1}{p}}\!\right)}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/39123c13bfd6b8be5d608f4889047c9219856f1e) |
gamma+
Sum[n=1 to ∞]
{ln(1-1/prime(n))
+1/prime(n)}
|
T ? |
ਫਰਮਾ:OEIS2C |
[0;3,1,4,1,2,5,2,1,1,1,1,13,4,2,4,2,1,33,296,...] |
1866 & 1873 |
0.26149721284764278375542683860869585 |
4.81047 73809 65351 65547 |
John constant[125] |
|
![{\displaystyle \gamma }](//wikimedia.org/api/rest_v1/media/math/render/svg/a223c880b0ce3da8f64ee33c4f0010beee400b1a) |
![{\displaystyle {\sqrt[{i}]{i}}=i^{-i}=(i^{i})^{-1}=(((i)^{i})^{i})^{i}=e^{\frac {\pi }{2}}={\sqrt {\sum _{n=0}^{\infty }{\frac {\pi ^{n}}{n!}}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/6748ac285bacbf5898f12507d0b1006bcfac2865) |
|
T |
ਫਰਮਾ:OEIS2C |
[4;1,4,3,1,1,1,1,1,1,1,1,7,1,20,1,3,6,10,3,2,...] |
|
4.81047738096535165547303566670383313 |
-0.5 ± 0.86602 54037 84438 64676 i |
Cube Root of 1[126] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/3/39/3rd_roots_of_unity.svg/100px-3rd_roots_of_unity.svg.png) |
![{\displaystyle {\sqrt[{3}]{1}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/911022b24127c88770950e9ebfe48fbd12d3fddf) |
![{\displaystyle {\begin{cases}\ \ 1\\-{\frac {1}{2}}+{\frac {\sqrt {3}}{2}}i\\-{\frac {1}{2}}-{\frac {\sqrt {3}}{2}}i.\end{cases}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/c288a56c0721bda10519be6b1b7cf65b80157d6e) |
1,
E^(2i pi/3),
E^(-2i pi/3)
|
C A |
ਫਰਮਾ:OEIS2C |
- [0,5] ± [0;1,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,...] i - [0,5] ± [0; 1, 6, 2] i |
|
- 0.5 ± 0.8660254037844386467637231707529 i |
0.11000 10000 00000 00000 0001 [Mw 113] |
Liouville number[127] |
|
![{\displaystyle {\text{£}}_{Li}}](//wikimedia.org/api/rest_v1/media/math/render/svg/ea5586b9e379c3c1252115ea9e350fa4d870b71c) |
![{\displaystyle \sum _{n=1}^{\infty }{\frac {1}{10^{n!}}}={\frac {1}{10^{1!}}}+{\frac {1}{10^{2!}}}+{\frac {1}{10^{3!}}}+{\frac {1}{10^{4!}}}+\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/13c8932cef345a057a73c6d0d38ffa848a59a6f9) |
|
T |
ਫਰਮਾ:OEIS2C |
[1;9,1,999,10,9999999999999,1,9,999,1,9] |
|
0.11000100000000000000000100... |
0.06598 80358 45312 53707[Mw 114] |
Lower limit of Tetration[128] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Infinite_power_tower.svg/80px-Infinite_power_tower.svg.png) |
![{\displaystyle {e}^{-e}}](//wikimedia.org/api/rest_v1/media/math/render/svg/cb10b1a7bc3bf2bdef3a1a1827d2853abef6e65d) |
![{\displaystyle \left({\frac {1}{e}}\right)^{e}}](//wikimedia.org/api/rest_v1/media/math/render/svg/1bd78fd090216eb624a593a2d27039c6afa09284) |
|
|
ਫਰਮਾ:OEIS2C |
[0;15,6,2,13,1,3,6,2,1,1,5,1,1,1,9,4,1,1,1,...] |
|
0.06598803584531253707679018759684642 |
1.83928 67552 14161 13255 |
Tribonacci constant[129] |
|
![{\displaystyle {\phi _{}}_{3}}](//wikimedia.org/api/rest_v1/media/math/render/svg/7b3dcd4454ecb4697d4c36dfb503e33902e5ad48) |
![{\displaystyle \textstyle {\frac {1+{\sqrt[{3}]{19+3{\sqrt {33}}}}+{\sqrt[{3}]{19-3{\sqrt {33}}}}}{3}}=\scriptstyle \,1+\left({\sqrt[{3}]{{\tfrac {1}{2}}+{\sqrt[{3}]{{\tfrac {1}{2}}+{\sqrt[{3}]{{\tfrac {1}{2}}+...}}}}}}\right)^{-1}}](//wikimedia.org/api/rest_v1/media/math/render/svg/dae9951b8fe98213be5c592eca8d81e10dcbc441) |
(1/3)*(1+(19+3
*sqrt(33))^(1/3)
+(19-3
*sqrt(33))^(1/3))
|
A |
ਫਰਮਾ:OEIS2C |
[1;1,5,4,2,305,1,8,2,1,4,6,14,3,1,13,5,1,7,...] |
|
1.83928675521416113255185256465328660 |
0.36651 29205 81664 32701 |
Median of the Gumbel distribution[130] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/5/51/GumbelDichteF.svg/100px-GumbelDichteF.svg.png) |
![{\displaystyle {ll_{2}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/4acba0d496554c6940b7783b3eebee129e7a4f1a) |
![{\displaystyle -\ln(\ln(2))}](//wikimedia.org/api/rest_v1/media/math/render/svg/e9b13dbf4de4363f47324799ff629f1456d09cba) |
|
|
A074785 |
[0;2,1,2,1,2,6,1,6,6,2,2,2,1,12,1,8,1,1,3,1,...] |
|
0.36651292058166432701243915823266947 |
36.46215 96072 07911 7709 |
Pi^pi[131] |
|
![{\displaystyle \pi ^{\pi }}](//wikimedia.org/api/rest_v1/media/math/render/svg/fca51740a9e8de79288a41996457b7f76861bc9a) |
![{\displaystyle \pi ^{\pi }}](//wikimedia.org/api/rest_v1/media/math/render/svg/fca51740a9e8de79288a41996457b7f76861bc9a) |
|
|
ਫਰਮਾ:OEIS2C |
[36;2,6,9,2,1,2,5,1,1,6,2,1,291,1,38,50,1,2,...] |
|
36.4621596072079117709908260226921236 |
0.53964 54911 90413 18711 |
Ioachimescu constant[132] |
|
![{\displaystyle 2+\zeta ({\tfrac {1}{2}})}](//wikimedia.org/api/rest_v1/media/math/render/svg/70326579c7934f90a230c3ca6a32b8e582e38098) |
![{\displaystyle {2{-}(1{+}{\sqrt {2}})\sum _{n=1}^{\infty }{\frac {(-1)^{n+1}}{\sqrt {n}}}}=\gamma +\sum _{n=1}^{\infty }{\frac {(-1)^{2n}\;\gamma _{n}}{2^{n}n!}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/b538fbe5a452f7f622353ca5145053af5c07be94) |
γ + N[
sum[n=1 to ∞]
{((-1)^(2n)
gamma_n)
/(2^n n!)}]
|
|
2- ਫਰਮਾ:OEIS2C |
[0;1,1,5,1,4,6,1,1,2,6,1,1,2,1,1,1,37,3,2,1,...] |
|
0.53964549119041318711050084748470198 |
15.15426 22414 79264 1897[Mw 115] |
Exponential reiterated constant[133] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Exp-esc.png/100px-Exp-esc.png) |
![{\displaystyle e^{e}}](//wikimedia.org/api/rest_v1/media/math/render/svg/6b2eaafb7132378e304dd42d23dc9cc97c5e78bc) |
![{\displaystyle \sum _{n=0}^{\infty }{\frac {e^{n}}{n!}}=\lim _{n\to \infty }\left({\frac {1+n}{n}}\right)^{n^{-n}(1+n)^{1+n}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/cf62a2d533d12cc3e5c02d872551c51e641c0b79) |
|
|
ਫਰਮਾ:OEIS2C |
[15;6,2,13,1,3,6,2,1,1,5,1,1,1,9,4,1,1,1,6,7,...] |
|
15.1542622414792641897604302726299119 |
0.64624 54398 94813 30426[Mw 116] |
Masser–Gramain constant[134] |
|
![{\displaystyle {C}}](//wikimedia.org/api/rest_v1/media/math/render/svg/7d9247343616c7631c19c44d199b0e0fce1847ad) |
![{\displaystyle \scriptstyle \beta ()={\text{Beta function}},\quad \scriptstyle \Gamma ()={\text{Gamma function}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/c5156dfe408fa9747e15233a0a7b59d99c7c2487)
|
Pi/4*(2*Gamma
+ 2*Log[2]
+ 3*Log[Pi]- 4
Log[Gamma[1/4]])
|
|
ਫਰਮਾ:OEIS2C |
[0;1,1,1,4,1,3,2,3,9,1,33,1,4,3,3,5,3,1,3,4,...] |
|
0.64624543989481330426647339684579279 |
1.11072 07345 39591 56175[Mw 117] |
The ratio of a square and circle circumscribed[135] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Circumscribed2.png/100px-Circumscribed2.png) |
![{\displaystyle {\frac {\pi }{2{\sqrt {2}}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/a95ec1404a0df3e29da316f53363f1a81f9b2990) |
![{\displaystyle \sum _{n=1}^{\infty }{\frac {({-}1)^{\lfloor {\frac {n-1}{2}}\rfloor }}{2n+1}}={\frac {1}{1}}+{\frac {1}{3}}-{\frac {1}{5}}-{\frac {1}{7}}+{\frac {1}{9}}+{\frac {1}{11}}-{\cdots }}](//wikimedia.org/api/rest_v1/media/math/render/svg/5985f4318285c9d1d1018ab116385f5c5ea4f705) |
sum[n=1 to ∞]
{(-1)^(floor(
(n-1)/2))
/(2n-1)}
|
T |
ਫਰਮਾ:OEIS2C |
[1;9,31,1,1,17,2,3,3,2,3,1,1,2,2,1,4,9,1,3,...] |
|
1.11072073453959156175397024751517342 |
1.45607 49485 82689 67139[Mw 118] |
Backhouse's constant[136] |
|
![{\displaystyle {B}}](//wikimedia.org/api/rest_v1/media/math/render/svg/caa14c36534651c09ba3f017ad210a1c4abe4b8c) |
![{\displaystyle P(x)=\sum _{k=1}^{\infty }{\underset {p_{k}{\text{ prime}}}{p_{k}x^{k}}}=1+2x+3x^{2}+5x^{3}+\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/96b3b698a061e41258b9f29e50f86a0e166662aa)
|
1/(FindRoot[0 == 1 +
Sum[x^n Prime[n],
{n, 10000}], {x, {1}})
|
|
ਫਰਮਾ:OEIS2C |
[1;2,5,5,4,1,1,18,1,1,1,1,1,2,13,3,1,2,4,16,...] |
1995 |
1.45607494858268967139959535111654355 |
1.85193 70519 82466 17036[Mw 119] |
Gibbs constant[137] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Sine_integral.svg/100px-Sine_integral.svg.png) |
Sin integral |
![{\displaystyle =\pi -{\frac {\pi ^{3}}{3\cdot 3!}}+{\frac {\pi ^{5}}{5\cdot 5!}}-{\frac {\pi ^{7}}{7\cdot 7!}}+\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/6a4428a4377d848f1459abaf2d43541c3b924c48)
|
|
|
ਫਰਮਾ:OEIS2C |
[1;1,5,1,3,15,1,5,3,2,7,2,1,62,1,3,110,1,39,...] |
|
1.85193705198246617036105337015799136 |
0.23571 11317 19232 93137[Mw 120] |
Copeland–Erdős constant[138] |
|
![{\displaystyle {{\mathcal {C}}_{CE}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/d9f85c607a73b62e591d49b2e5bb40645ec79223) |
![{\displaystyle \sum _{n=1}^{\infty }{\frac {p_{n}}{10^{n+\sum \limits _{k=1}^{n}\lfloor \log _{10}{p_{k}}\rfloor }}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/167297822a353ea78c1699606f25a658f4b9e62b) |
sum[n=1 to ∞]
{prime(n) /(n+(10^
sum[k=1 to n]{floor
(log_10 prime(k))}))}
|
I |
ਫਰਮਾ:OEIS2C |
[0;4,4,8,16,18,5,1,1,1,1,7,1,1,6,2,9,58,1,3,...] |
|
0.23571113171923293137414347535961677 |
1.52362 70862 02492 10627[Mw 121] |
Fractal dimension of the boundary of the dragon curve[139] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Fractal_dragon_curve.jpg/100px-Fractal_dragon_curve.jpg) |
![{\displaystyle {C_{d}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/d91e04652c1977511baafeaa8cdbc6e9e43deee9) |
![{\displaystyle {\frac {\log \left({\frac {1+{\sqrt[{3}]{73-6{\sqrt {87}}}}+{\sqrt[{3}]{73+6{\sqrt {87}}}}}{3}}\right)}{\log(2)}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/2a4162d90ad47ab451e6a198868b1d38f9a4f305) |
(log((1+(73-6 sqrt(87))^1/3+
(73+6 sqrt(87))^1/3)/3))/
log(2)))
|
T |
|
[1;1,1,10,12,2,1,149,1,1,1,3,11,1,3,17,4,1,...] |
|
1.52362708620249210627768393595421662 |
1.78221 39781 91369 11177[Mw 122] |
Grothendieck constant[140] |
|
![{\displaystyle {K_{R}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/22e43bc4f8d39b374b3c33cb0c2a06d420b12ea2) |
![{\displaystyle {\frac {\pi }{2\log(1+{\sqrt {2}})}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/9efb80c8972a889f544c0aef307d74f60b0deed2) |
|
|
ਫਰਮਾ:OEIS2C |
[1;1,3,1,1,2,4,2,1,1,17,1,12,4,3,5,10,1,1,3,...] |
|
1.78221397819136911177441345297254934 |
1.58496 25007 21156 18145[Mw 123] |
Hausdorff dimension, Sierpinski triangle[141] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/2/27/SierpinskiTriangle-ani-0-7.gif/100px-SierpinskiTriangle-ani-0-7.gif) |
![{\displaystyle {log_{2}3}}](//wikimedia.org/api/rest_v1/media/math/render/svg/aef1802d45ed0d2633a5952d7d19a345e83ce8b5) |
![{\displaystyle {\frac {\log 3}{\log 2}}={\frac {\sum _{n=0}^{\infty }{\frac {1}{2^{2n+1}(2n+1)}}}{\sum _{n=0}^{\infty }{\frac {1}{3^{2n+1}(2n+1)}}}}={\frac {{\frac {1}{2}}+{\frac {1}{24}}+{\frac {1}{160}}+\cdots }{{\frac {1}{3}}+{\frac {1}{81}}+{\frac {1}{1215}}+\cdots }}}](//wikimedia.org/api/rest_v1/media/math/render/svg/b63cd2bef71039491622a8460dd91f8f0b173cef) |
(Sum[n=0 to ∞] {1/
(2^(2n+1) (2n+1))})/
(Sum[n=0 to ∞] {1/
(3^(2n+1) (2n+1))})
|
T |
ਫਰਮਾ:OEIS2C |
[1;1,1,2,2,3,1,5,2,23,2,2,1,1,55,1,4,3,1,1,...] |
|
1.58496250072115618145373894394781651 |
1.30637 78838 63080 69046[Mw 124] |
Mills' constant[142] |
|
![{\displaystyle {\theta }}](//wikimedia.org/api/rest_v1/media/math/render/svg/0f27c7ca81c352a90aa39ab1c7a5a3aea3f0ae06) |
primes |
Nest[ NextPrime[#^3] &, 2, 7]^(1/3^8)
|
|
ਫਰਮਾ:OEIS2C |
[1;3,3,1,3,1,2,1,2,1,4,2,35,21,1,4,4,1,1,3,2,...] |
1947 |
1.30637788386308069046861449260260571 |
2.02988 32128 19307 25004[Mw 125] |
Figure eight knot hyperbolic volume[143] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Blue_Figure-Eight_Knot.png/100px-Blue_Figure-Eight_Knot.png) |
![{\displaystyle {V_{8}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/5e417440db1b084c601ad14ac3458cd652240573) |
![{\displaystyle \scriptstyle {\frac {\sqrt {3}}{9}}\,\sum \limits _{n=0}^{\infty }{\frac {(-1)^{n}}{27^{n}}}\,\left\{\!{\frac {18}{(6n+1)^{2}}}-{\frac {18}{(6n+2)^{2}}}-{\frac {24}{(6n+3)^{2}}}-{\frac {6}{(6n+4)^{2}}}+{\frac {2}{(6n+5)^{2}}}\!\right\}}](//wikimedia.org/api/rest_v1/media/math/render/svg/13dce1395ab688509f978f2b1f3aeb125135908b)
|
6 integral[0 to pi/3]
{log(1/(2 sin (n)))}
|
|
ਫਰਮਾ:OEIS2C |
[2;33,2,6,2,1,2,2,5,1,1,7,1,1,1,113,1,4,5,1,...] |
|
2.02988321281930725004240510854904057 |
262 53741 26407 68743 .99999 99999 99250 073[Mw 126] |
Hermite–Ramanujan constant[144] |
|
![{\displaystyle {R}}](//wikimedia.org/api/rest_v1/media/math/render/svg/3abe7f424f59ed9925c7f622af7aead87831412b) |
![{\displaystyle e^{\pi {\sqrt {163}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/74fd61cac30067a5b97427918bbc23b1f310115f) |
|
T |
ਫਰਮਾ:OEIS2C |
[262537412640768743;1,1333462407511,1,8,1,1,5,...] |
1859 |
262537412640768743.999999999999250073 |
1.74540 56624 07346 86349[Mw 127] |
Khinchin harmonic mean[145] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Plot_harmonic_mean.png/100px-Plot_harmonic_mean.png) |
![{\displaystyle {K_{-1}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/ed9049ff2452c953a2fd8442345d010f252dafaa) |
a1 ... an are elements of a continued fraction [a0; a1, a2, ..., an] |
(log 2)/
(sum[n=1 to ∞]
{1/n log(1+
1/(n(n+2))}
|
|
ਫਰਮਾ:OEIS2C |
[1;1,2,1,12,1,5,1,5,13,2,13,2,1,9,1,6,1,3,1,...] |
|
1.74540566240734686349459630968366106 |
1.64872 12707 00128 14684[Ow 5] |
Square root of the number e[146] |
|
![{\displaystyle {\sqrt {e}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/95416e44d6a75cda0c0b059e5bec517849f63dd3) |
![{\displaystyle \sum _{n=0}^{\infty }{\frac {1}{2^{n}n!}}=\sum _{n=0}^{\infty }{\frac {1}{(2n)!!}}={\frac {1}{1}}+{\frac {1}{2}}+{\frac {1}{8}}+{\frac {1}{48}}+\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/2146f04eb87a7e9ad04a7303537815ee17190350) |
Sum[n=0 to ∞]
{1/(2^n n!)}
|
T |
ਫਰਮਾ:OEIS2C |
[1;1,1,1,5,1,1,9,1,1,13,1,1,17,1,1,21,1,1,...] = [1;1,1,1,4p+1], p∈ℕ |
|
1.64872127070012814684865078781416357 |
1.01734 30619 84449 13971[Mw 128] |
Zeta(6)[147] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Zeta.png/100px-Zeta.png) |
![{\displaystyle \zeta (6)}](//wikimedia.org/api/rest_v1/media/math/render/svg/292726d53a082e54c125574dfe95b577b27487b2) |
![{\displaystyle {\frac {\pi ^{6}}{945}}\!=\!\prod _{n=1}^{\infty }\!{\underset {p_{n}:{\text{ prime}}}{\frac {1}{{1-p_{n}}^{-6}}}}={\frac {1}{1\!-\!2^{-6}}}\!\cdot \!{\frac {1}{1\!-\!3^{-6}}}\!\cdot \!{\frac {1}{1\!-\!5^{-6}}}\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/1a576354f48903bb72ff25289c962b719eb3834f) |
Prod[n=1 to ∞]
{1/(1-ithprime
(n)^-6)}
|
T |
ਫਰਮਾ:OEIS2C |
[1;57,1,1,1,15,1,6,3,61,1,5,3,1,6,1,3,3,6,1,...] |
|
1.01734306198444913971451792979092052 |
0.10841 01512 23111 36151[Mw 129] |
Trott constant[148] |
|
![{\displaystyle \mathrm {T} _{1}}](//wikimedia.org/api/rest_v1/media/math/render/svg/8a84c16f87b47075471894b03dd81a73987a924d) |
![{\displaystyle {\tfrac {1}{1+{\tfrac {1}{0+{\tfrac {1}{8+{\tfrac {1}{4+{\tfrac {1}{1+{\tfrac {1}{0+1{/\cdots }}}}}}}}}}}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/95c5b57fc949fe3c5f30e52091377d16c21ab002)
|
|
|
ਫਰਮਾ:OEIS2C |
[0;9,4,2,5,1,2,2,3,1,1,1,3,6,1,5,1,1,2,...] |
|
0.10841015122311136151129081140641509 |
0.00787 49969 97812 3844[Mw 130] |
Chaitin constant[149] |
![](//upload.wikimedia.org/wikipedia/commons/thumb/b/bd/ProgramTree.svg/40px-ProgramTree.svg.png) |
![{\displaystyle \Omega }](//wikimedia.org/api/rest_v1/media/math/render/svg/24b0d5ca6f381068d756f6337c08e0af9d1eeb6f) |
- p: Halted program
- | p |: Size in bits of program p
- P: Domain of all programs that stop.
See also: Halting problem |
|
T |
ਫਰਮਾ:OEIS2C |
[0; 126, 1, 62, 5, 5, 3, 3, 21, 1, 4, 1] |
1975 |
0.0078749969978123844 |
0.83462 68416 74073 18628[Mw 131] |
Gauss constant[150] |
|
![{\displaystyle {G}}](//wikimedia.org/api/rest_v1/media/math/render/svg/f054c7208d06606d0d033b7ae5eb578bfb66aec3) |
AGM = Arithmetic–geometric mean |
(4 sqrt(2)((1/4)!)^2)
/pi^(3/2)
|
T |
ਫਰਮਾ:OEIS2C |
[0;1,5,21,3,4,14,1,1,1,1,1,3,1,15,1,3,7,1,...] |
|
0.83462684167407318628142973279904680 |
1.45136 92348 83381 05028[Mw 132] |
Ramanujan–Soldner constant[151][152] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Integrallogrithm.png/100px-Integrallogrithm.png) |
![{\displaystyle {\mu }}](//wikimedia.org/api/rest_v1/media/math/render/svg/fb2e32303f97e0988fc733de21d8fb57cc12360f) |
li = Logarithmic integral
Ei = Exponential integral
|
|
I |
ਫਰਮਾ:OEIS2C |
[1;2,4,1,1,1,3,1,1,1,2,47,2,4,1,12,1,1,2,2,1,...] |
1792 to 1809 |
1.45136923488338105028396848589202744 |
0.64341 05462 88338 02618[Mw 133] |
Cahen's constant[153] |
|
![{\displaystyle \xi _{2}}](//wikimedia.org/api/rest_v1/media/math/render/svg/837e12bb12fde6a1a8f6585a7e56635b4c7113d1) |
Where sk is the kth term of Sylvester's sequence 2, 3, 7, 43, 1807, ...
Defined as: ![{\displaystyle \,\,S_{0}=\,2,\,\,S_{k}=\,1+\prod \limits _{n=0}^{k-1}S_{n}{\text{ for}}\;k>0}](//wikimedia.org/api/rest_v1/media/math/render/svg/1f78fdd95b4cdc22689981aee883e33412d01e9c) |
|
T |
ਫਰਮਾ:OEIS2C |
[0; 1, 1, 1, 4, 9, 196, 16641, 639988804, ...] |
1891 |
0.64341054628833802618225430775756476 |
1.41421 35623 73095 04880[Mw 134] |
Square root of 2, Pythagoras constant.[154] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Square_root_of_2_triangle.svg/100px-Square_root_of_2_triangle.svg.png) |
![{\displaystyle {\sqrt {2}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/b4afc1e27d418021bf10898eb44a7f5f315735ff) |
![{\displaystyle \!\prod _{n=1}^{\infty }\!\left(1\!+\!{\frac {(-1)^{n+1}}{2n-1}}\right)\!=\!\left(1\!+\!{\frac {1}{1}}\right)\!\left(1\!-\!{\frac {1}{3}}\right)\!\left(1\!+\!{\frac {1}{5}}\right)\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/c42cb171646bfa90185c634a75ff418a6161813a) |
prod[n=1 to ∞]
{1+(-1)^(n+1)
/(2n-1)}
|
A |
ਫਰਮਾ:OEIS2C |
[1;2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,...] = [1;2...] |
|
1.41421356237309504880168872420969808 |
1.77245 38509 05516 02729[Mw 135] |
Carlson–Levin constant[117] |
|
![{\displaystyle {\Gamma }({\tfrac {1}{2}})}](//wikimedia.org/api/rest_v1/media/math/render/svg/e33da04209e4e12699e91aee39178ee3735c9268) |
![{\displaystyle {\sqrt {\pi }}=\left(-{\frac {1}{2}}\right)!=\int _{-\infty }^{\infty }{\frac {1}{e^{x^{2}}}}\,dx=\int _{0}^{1}{\frac {1}{\sqrt {-\ln x}}}\,dx}](//wikimedia.org/api/rest_v1/media/math/render/svg/8f550052e67d7275ca02b1f88a36ac2dfb82f88f) |
|
T |
ਫਰਮਾ:OEIS2C |
[1;1,3,2,1,1,6,1,28,13,1,1,2,18,1,1,1,83,1,...] |
|
1.77245385090551602729816748334114518 |
1.05946 30943 59295 26456[Ow 6] |
Musical interval between each half tone[155][156] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/YB0214_Clavier_tempere.png/100px-YB0214_Clavier_tempere.png)
|
![{\displaystyle {\sqrt[{12}]{2}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/bc835f27425fb3140e1f75a5faa35b1e8b9efc35) |
(A = 440 Hz) |
|
A |
ਫਰਮਾ:OEIS2C |
[1;16,1,4,2,7,1,1,2,2,7,4,1,2,1,60,1,3,1,2,...] |
|
1.05946309435929526456182529494634170 |
1.01494 16064 09653 62502[Mw 136] |
Gieseking constant[157] |
|
![{\displaystyle {\pi \ln \beta }}](//wikimedia.org/api/rest_v1/media/math/render/svg/0b45295ee7435bc1510af06b76d6ccb49990227f) |
.
|
sqrt(3)*3/4 *(1
-Sum[n=0 to ∞]
{1/((3n+2)^2)}
+Sum[n=1 to ∞]
{1/((3n+1)^2)})
|
|
ਫਰਮਾ:OEIS2C |
[1;66,1,12,1,2,1,4,2,1,3,3,1,4,1,56,2,2,11,...] |
1912 |
1.01494160640965362502120255427452028 |
2.62205 75542 92119 81046[Mw 137] |
Lemniscate constant[158] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Lemniscate_of_Gerono.svg/100px-Lemniscate_of_Gerono.svg.png) |
![{\displaystyle {\varpi }}](//wikimedia.org/api/rest_v1/media/math/render/svg/a837f572966d3bf18f90bec415b117deb48e8559) |
![{\displaystyle \pi \,{G}=4{\sqrt {\tfrac {2}{\pi }}}\,\Gamma {\left({\tfrac {5}{4}}\right)^{2}}={\tfrac {1}{4}}{\sqrt {\tfrac {2}{\pi }}}\,\Gamma {\left({\tfrac {1}{4}}\right)^{2}}=4{\sqrt {\tfrac {2}{\pi }}}\left({\tfrac {1}{4}}!\right)^{2}}](//wikimedia.org/api/rest_v1/media/math/render/svg/b7347512d594da8df8ef7d6dc05c31c740d6240d) |
|
T |
ਫਰਮਾ:OEIS2C |
[2;1,1,1,1,1,4,1,2,5,1,1,1,14,9,2,6,2,9,4,1,...] |
1798 |
2.62205755429211981046483958989111941 |
1.28242 71291 00622 63687[Mw 138] |
Glaisher–Kinkelin constant |
|
![{\displaystyle {A}}](//wikimedia.org/api/rest_v1/media/math/render/svg/f5ebb239b453149a6dedba8f18670ce9a9390c08) |
![{\displaystyle e^{{\frac {1}{12}}-\zeta ^{\prime }(-1)}=e^{{\frac {1}{8}}-{\frac {1}{2}}\sum \limits _{n=0}^{\infty }{\frac {1}{n+1}}\sum \limits _{k=0}^{n}\left(-1\right)^{k}{\binom {n}{k}}\left(k+1\right)^{2}\ln(k+1)}}](//wikimedia.org/api/rest_v1/media/math/render/svg/cb3436ba9f68e35048a9c70cddd80a7726701a81) |
|
T ? |
ਫਰਮਾ:OEIS2C |
[1;3,1,1,5,1,1,1,3,12,4,1,271,1,1,2,7,1,35,...] |
|
1.28242712910062263687534256886979172 |
-4.22745 35333 76265 408[Mw 139] |
Digamma (1/4)[159] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/6/68/Complex_Polygamma_0.jpg/100px-Complex_Polygamma_0.jpg) |
![{\displaystyle {\psi }({\tfrac {1}{4}})}](//wikimedia.org/api/rest_v1/media/math/render/svg/352ae5b3a815744ff8060eb1572bf994e31fdc5e) |
![{\displaystyle -\gamma -{\frac {\pi }{2}}-3\ln {2}=-\gamma +\sum _{n=0}^{\infty }\left({\frac {1}{n+1}}-{\frac {1}{n+{\tfrac {1}{4}}}}\right)}](//wikimedia.org/api/rest_v1/media/math/render/svg/7f9ee975d2e55be2b263e7dd6979d92628f2a479) |
-EulerGamma
-\pi/2 -3 log 2
|
|
ਫਰਮਾ:OEIS2C |
-[4;4,2,1,1,10,1,5,9,11,1,22,1,1,14,1,2,1,4,...] |
|
-4.2274535333762654080895301460966835 |
0.28674 74284 34478 73410[Mw 140] |
Strongly Carefree constant[160] |
|
![{\displaystyle K_{2}}](//wikimedia.org/api/rest_v1/media/math/render/svg/57e1b324cf5b68f2729a8634ff76e396b634b75d) |
![{\displaystyle \prod _{n=1}^{\infty }{\underset {p_{n}:{\text{ prime}}}{\left(1-{\frac {3p_{n}-2}{{p_{n}}^{3}}}\right)}}={\frac {6}{\pi ^{2}}}\prod _{n=1}^{\infty }{\underset {p_{n}:{\text{ prime}}}{\left(1-{\frac {1}{p_{n}(p_{n}+1)}}\right)}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/d07e2466c8f74458499c7caa81a5f6fb4e1ac056) |
N[ prod[k=1 to ∞]
{1-(3*prime(k)-2)
/(prime(k)^3)}]
|
|
ਫਰਮਾ:OEIS2C |
[0;3,2,19,3,12,1,5,1,5,1,5,2,1,1,1,1,1,3,7,...] |
|
0.28674742843447873410789271278983845 |
3.62560 99082 21908 31193[Mw 141] |
Gamma(1/4)[161] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Gamma_abs_3D.png/100px-Gamma_abs_3D.png) |
![{\displaystyle \Gamma ({\tfrac {1}{4}})}](//wikimedia.org/api/rest_v1/media/math/render/svg/1b4b2f765d1161c27e78192ffadefacb2c2d362e) |
![{\displaystyle 4\left({\frac {1}{4}}\right)!=\left(-{\frac {3}{4}}\right)!}](//wikimedia.org/api/rest_v1/media/math/render/svg/b80637aa7c7f9669e875d1508036213d3b5fc6ad) |
|
T |
ਫਰਮਾ:OEIS2C |
[3;1,1,1,2,25,4,9,1,1,8,4,1,6,1,1,19,1,1,4,1,...] |
1729 |
3.62560990822190831193068515586767200 |
1.66168 79496 33594 12129[Mw 142] |
Somos' quadratic recurrence constant[162] |
|
![{\displaystyle {\sigma }}](//wikimedia.org/api/rest_v1/media/math/render/svg/314ac5cfd38ebefe34513c781f56fa6510fa4fb6) |
![{\displaystyle \prod _{n=1}^{\infty }n^{{1/2}^{n}}={\sqrt {1{\sqrt {2{\sqrt {3\cdots }}}}}}=1^{1/2}\;2^{1/4}\;3^{1/8}\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/bfcd0a276ed5aa23134e3721a3acd38df9cb01e2) |
prod[n=1 to ∞]
{n ^(1/2)^n}
|
T ? |
ਫਰਮਾ:OEIS2C |
[1;1,1,1,21,1,1,1,6,4,2,1,1,2,1,3,1,13,13,...] |
|
1.66168794963359412129581892274995074 |
0.95531 66181 245092 78163 |
Magic angle[163] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Magic_angle.png/100px-Magic_angle.png) |
![{\displaystyle {\theta _{m}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/933a1508bfd776a9f0ddac97828c92fde21e75d5) |
![{\displaystyle \arctan \left({\sqrt {2}}\right)=\arccos \left({\sqrt {\tfrac {1}{3}}}\right)\approx \textstyle {54.7356}^{\circ }}](//wikimedia.org/api/rest_v1/media/math/render/svg/328d7633dcf27d0da868a2aced99a8a510624507) |
|
T |
ਫਰਮਾ:OEIS2C |
[0;1,21,2,1,1,1,2,1,2,2,4,1,2,9,1,2,1,1,1,3,...] |
|
0.95531661812450927816385710251575775 |
1.78107 24179 90197 98523[Mw 143] |
Exp.gamma, Barnes G-function[164] |
|
![{\displaystyle e^{\gamma }}](//wikimedia.org/api/rest_v1/media/math/render/svg/a15141c220223dbd2dcad746e6907b20ff6b1328) |
![{\displaystyle \textstyle \left({\frac {2}{1}}\right)^{1/2}\left({\frac {2^{2}}{1\cdot 3}}\right)^{1/3}\left({\frac {2^{3}\cdot 4}{1\cdot 3^{3}}}\right)^{1/4}\left({\frac {2^{4}\cdot 4^{4}}{1\cdot 3^{6}\cdot 5}}\right)^{1/5}\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/b7e80348ae956a893b7f1019eb521728e8984bc2)
|
Prod[n=1 to ∞]
{e^(1/n)}
/{1 + 1/n}
|
|
ਫਰਮਾ:OEIS2C |
[1;1,3,1,1,3,5,4,1,1,2,2,1,7,9,1,16,1,1,1,2,...] |
|
1.78107241799019798523650410310717954 |
0.74759 79202 53411 43517[Mw 144] |
Rényi's Parking Constant[165] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/ParallelParkingAnimation2.gif/100px-ParallelParkingAnimation2.gif) |
![{\displaystyle {m}}](//wikimedia.org/api/rest_v1/media/math/render/svg/989d8ed6300d470470571f438bbe51f0693fb7b2) |
![{\displaystyle \int \limits _{0}^{\infty }exp\left(\!-2\int \limits _{0}^{x}{\frac {1-e^{-y}}{y}}dy\right)\!dx={e^{-2\gamma }}\int \limits _{0}^{\infty }{\frac {e^{-2\Gamma (0,n)}}{n^{2}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/3a0da95adf4d6d39955f7991ad7e40ba4bf59bfa) |
[e^(-2*Gamma)]
*।nt{n,0,∞}[ e^(- 2
*Gamma(0,n)) /n^2]
|
|
ਫਰਮਾ:OEIS2C |
[0;1,2,1,25,3,1,2,1,1,12,1,2,1,1,3,1,2,1,43,...] |
|
0.74759792025341143517873094383017817 |
1.27323 95447 35162 68615 |
Ramanujan–Forsyth series[166] |
|
![{\displaystyle {\frac {4}{\pi }}}](//wikimedia.org/api/rest_v1/media/math/render/svg/97a23c0217f06a368bacaba22afe66b83374f3b3) |
![{\displaystyle \displaystyle \sum \limits _{n=0}^{\infty }\textstyle \left({\frac {(2n-3)!!}{(2n)!!}}\right)^{2}={1\!+\!\left({\frac {1}{2}}\right)^{2}\!+\!\left({\frac {1}{2\cdot 4}}\right)^{2}\!+\!\left({\frac {1\cdot 3}{2\cdot 4\cdot 6}}\right)^{2}+\cdots }}](//wikimedia.org/api/rest_v1/media/math/render/svg/d3ede324f4b6edbf98709e80367f3839785c3116) |
Sum[n=0 to ∞]
{[(2n-3)!!
/(2n)!!]^2}
|
I |
ਫਰਮਾ:OEIS2C |
[1;3,1,1,1,15,2,72,1,9,1,17,1,2,1,5,1,1,10,...] |
|
1.27323954473516268615107010698011489 |
1.44466 78610 09766 13365[Mw 145] |
Steiner number, Iterated exponential Constant[167] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Infinite_power_tower.svg/80px-Infinite_power_tower.svg.png) |
![{\displaystyle {\sqrt[{e}]{e}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/96733766fde42bf61b329fba3cc27c54f46b21e5) |
= Upper Limit of Tetration |
|
T |
ਫਰਮਾ:OEIS2C |
[1;2,4,55,27,1,1,16,9,3,2,8,3,2,1,1,4,1,9,...] |
|
1.44466786100976613365833910859643022 |
0.69220 06275 55346 35386[Mw 146] |
Minimum value of función ƒ(x) = xx[168] |
|
![{\displaystyle {\left({\frac {1}{e}}\right)}^{\frac {1}{e}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/d24a579ed0e7758fb981a34fe01dcb300ba39418) |
=।nverse Steiner Number |
|
|
ਫਰਮਾ:OEIS2C |
[0;1,2,4,55,27,1,1,16,9,3,2,8,3,2,1,1,4,1,9,...] |
|
0.69220062755534635386542199718278976 |
0.34053 73295 50999 14282[Mw 147] |
Pólya Random walk constant[169] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Walk3d_0.png/100px-Walk3d_0.png) |
![{\displaystyle {p(3)}}](//wikimedia.org/api/rest_v1/media/math/render/svg/80defd15f8526515cbc545cf3a39140ba3dd3d8f) |
![{\displaystyle =1-16{\sqrt {\tfrac {2}{3}}}\;\pi ^{3}\left(\Gamma ({\tfrac {1}{24}})\Gamma ({\tfrac {5}{24}})\Gamma ({\tfrac {7}{24}})\Gamma ({\tfrac {11}{24}})\right)^{-1}}](//wikimedia.org/api/rest_v1/media/math/render/svg/70c06bcb7cfe04a4911db6b6dd25b0b5cc9f41e8)
|
1-16*Sqrt[2/3]*Pi^3
/(Gamma[1/24]
*Gamma[5/24]
*Gamma[7/24]
*Gamma[11/24])
|
|
ਫਰਮਾ:OEIS2C |
[0;2,1,14,1,3,8,1,5,2,7,1,12,1,5,59,1,1,1,3,...] |
|
0.34053732955099914282627318443290289 |
0.54325 89653 42976 70695[Mw 148] |
Bloch–Landau constant[170] |
|
![{\displaystyle {L}}](//wikimedia.org/api/rest_v1/media/math/render/svg/bb611299dffc63232ed1fc05560afc3f1dd3d005) |
![{\displaystyle ={\frac {\Gamma ({\tfrac {1}{3}})\;\Gamma ({\tfrac {5}{6}})}{\Gamma ({\tfrac {1}{6}})}}={\frac {(-{\tfrac {2}{3}})!\;(-1+{\tfrac {5}{6}})!}{(-1+{\tfrac {1}{6}})!}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/f01eb4aa7b7b9e38891c281d395cf2f4b8e711c5) |
gamma(1/3)
*gamma(5/6)
/gamma(1/6)
|
|
ਫਰਮਾ:OEIS2C |
[0;1,1,5,3,1,1,2,1,1,6,3,1,8,11,2,1,1,27,4,...] |
1929 |
0.54325896534297670695272829530061323 |
0.18785 96424 62067 12024[Mw 149][Ow 7] |
MRB Constant, Marvin Ray Burns[171][172][173] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/MRB-Gif.gif/100px-MRB-Gif.gif) |
![{\displaystyle C_{{}_{MRB}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/37da536ae382f122694af3dc9bd13ac756609133) |
![{\displaystyle \sum _{n=1}^{\infty }(-1)^{n}(n^{1/n}-1)=-{\sqrt[{1}]{1}}+{\sqrt[{2}]{2}}-{\sqrt[{3}]{3}}+\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/bf94fe4a0532c848df4279399c611feb19e39c99) |
Sum[n=1 to ∞]
{(-1)^n (n^(1/n)-1)}
|
|
ਫਰਮਾ:OEIS2C |
[0;5,3,10,1,1,4,1,1,1,1,9,1,1,12,2,17,2,2,1,...] |
1999 |
0.18785964246206712024851793405427323 |
1.46707 80794 33975 47289[Mw 150] |
Porter Constant[174] |
|
![{\displaystyle {C}}](//wikimedia.org/api/rest_v1/media/math/render/svg/7d9247343616c7631c19c44d199b0e0fce1847ad) |
![{\displaystyle \scriptstyle \zeta '(2)\,{\text{= Derivative of }}\zeta (2)=-\sum \limits _{n=2}^{\infty }{\frac {\ln n}{n^{2}}}=-0.9375482543\ldots }](//wikimedia.org/api/rest_v1/media/math/render/svg/00ff1a6076b9ad5a91e40de73fe8da0842c25a78)
|
6*ln2/pi^2(3*ln2+
4 EulerGamma-
WeierstrassZeta'(2)
*24/pi^2-2)-1/2
|
|
ਫਰਮਾ:OEIS2C |
[1;2,7,10,1,2,38,5,4,1,4,12,5,1,5,1,2,3,1,...] |
1974 |
1.46707807943397547289779848470722995 |
4.66920 16091 02990 67185[Mw 151] |
Feigenbaum constant δ[175] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/LogisticMap_BifurcationDiagram.png/100px-LogisticMap_BifurcationDiagram.png) |
![{\displaystyle {\delta }}](//wikimedia.org/api/rest_v1/media/math/render/svg/cfa3b6ab8d308aa70d0e3a0db80710af6cae081f) |
![{\displaystyle \scriptstyle x_{n+1}=\,ax_{n}(1-x_{n})\quad {\text{or}}\quad x_{n+1}=\,a\sin(x_{n})}](//wikimedia.org/api/rest_v1/media/math/render/svg/6f42360735b5db563d3ee04d83ee86d2d368d278)
|
|
T |
ਫਰਮਾ:OEIS2C |
[4;1,2,43,2,163,2,3,1,1,2,5,1,2,3,80,2,5,...] |
1975 |
4.66920160910299067185320382046620161 |
2.50290 78750 95892 82228[Mw 152] |
Feigenbaum constant α[176] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Mandelbrot_zoom.gif/100px-Mandelbrot_zoom.gif) |
![{\displaystyle \alpha }](//wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3) |
![{\displaystyle \lim _{n\to \infty }{\frac {d_{n}}{d_{n+1}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/66f855b6530198ba5a419805a2eb48d0a2310e80) |
|
T ? |
ਫਰਮਾ:OEIS2C |
[2;1,1,85,2,8,1,10,16,3,8,9,2,1,40,1,2,3,...] |
1979 |
2.50290787509589282228390287321821578 |
0.62432 99885 43550 87099[Mw 153] |
Golomb–Dickman constant[177] |
|
![{\displaystyle {\lambda }}](//wikimedia.org/api/rest_v1/media/math/render/svg/80912e657954ba7a08dc822fac02fd5fd61067c1) |
![{\displaystyle \int \limits _{0}^{\infty }{\underset {{\text{Para }}x>2}{{\frac {f(x)}{x^{2}}}\,dx}}=\int \limits _{0}^{1}e^{\operatorname {Li} (n)}dn\quad \scriptstyle {\text{Li: Logarithmic integral}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/41035cb9316f4e2ad9461c58e11786d07c156b05) |
N[Int{n,0,1}[e^Li(n)],34]
|
|
ਫਰਮਾ:OEIS2C |
[0;1,1,1,1,1,22,1,2,3,1,1,11,1,1,2,22,2,6,1,...] |
1930 & 1964 |
0.62432998854355087099293638310083724 |
23.14069 26327 79269 0057[Mw 154] |
Gelfond constant[178] |
|
![{\displaystyle {e}^{\pi }}](//wikimedia.org/api/rest_v1/media/math/render/svg/25a1fc9a7153fbddaeda120876466e666d907e94) |
![{\displaystyle (-1)^{-i}=i^{-2i}=\sum _{n=0}^{\infty }{\frac {\pi ^{n}}{n!}}={\frac {\pi ^{1}}{1}}+{\frac {\pi ^{2}}{2!}}+{\frac {\pi ^{3}}{3!}}+\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/a64f31305946a6beeeeec45c2231b6fe3be75fd9) |
Sum[n=0 to ∞]
{(pi^n)/n!}
|
T |
ਫਰਮਾ:OEIS2C |
[23;7,9,3,1,1,591,2,9,1,2,34,1,16,1,30,1,...] |
|
23.1406926327792690057290863679485474
|
7.38905 60989 30650 22723 |
Conic constant, Schwarzschild constant[179] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Conic_constant.svg/100px-Conic_constant.svg.png) |
![{\displaystyle e^{2}}](//wikimedia.org/api/rest_v1/media/math/render/svg/806b2751f62ef9c86ca80e8d3c662ae5dd4d1c2d) |
![{\displaystyle \sum _{n=0}^{\infty }{\frac {2^{n}}{n!}}=1+2+{\frac {2^{2}}{2!}}+{\frac {2^{3}}{3!}}+{\frac {2^{4}}{4!}}+{\frac {2^{5}}{5!}}+\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/3809255ff99f207f7a7bf4345fc60e1712a38fe4) |
|
T |
ਫਰਮਾ:OEIS2C |
[7;2,1,1,3,18,5,1,1,6,30,8,1,1,9,42,11,1,...] = [7,2,1,1,n,4*n+6,n+2], n = 3, 6, 9, etc. |
|
7.38905609893065022723042746057500781 |
0.35323 63718 54995 98454[Mw 155] |
Hafner–Sarnak–McCurley constant (1)[180] |
|
![{\displaystyle {\sigma }}](//wikimedia.org/api/rest_v1/media/math/render/svg/314ac5cfd38ebefe34513c781f56fa6510fa4fb6) |
![{\displaystyle \prod _{k=1}^{\infty }\left\{1-[1-\prod _{j=1}^{n}{\underset {p_{k}:{\text{ prime}}}{(1-p_{k}^{-j})]^{2}}}\right\}}](//wikimedia.org/api/rest_v1/media/math/render/svg/29779ad935b6ca6841740b063171ce4a3031e70d) |
prod[k=1 to ∞]
{1-(1-prod[j=1 to n]
{1-ithprime(k)^-j})^2}
|
|
ਫਰਮਾ:OEIS2C |
[0;2,1,4,1,10,1,8,1,4,1,2,1,2,1,2,6,1,1,1,3,...] |
1993 |
0.35323637185499598454351655043268201 |
0.60792 71018 54026 62866[Mw 156] |
Hafner–Sarnak–McCurley constant (2)[181] |
|
![{\displaystyle {\frac {1}{\zeta (2)}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/185ba797b275c569fe8b021c716c61dc03435a9c) |
![{\displaystyle {\frac {6}{\pi ^{2}}}=\prod _{n=0}^{\infty }{\underset {p_{n}:{\text{ prime}}}{\!\left(\!1-{\frac {1}{{p_{n}}^{2}}}\!\right)}}\!=\!\textstyle \left(1\!-\!{\frac {1}{2^{2}}}\right)\!\left(1\!-\!{\frac {1}{3^{2}}}\right)\!\left(1\!-\!{\frac {1}{5^{2}}}\right)\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/66bb1a9b58a49a94a579544bf5cdfc8afad360f5) |
Prod{n=1 to ∞}
(1-1/ithprime(n)^2)
|
T |
ਫਰਮਾ:OEIS2C |
[0;1,1,1,1,4,2,4,7,1,4,2,3,4,10,1,2,1,1,1,...] |
|
0.60792710185402662866327677925836583 |
0.12345 67891 01112 13141[Mw 157] |
Champernowne constant[182] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/1/12/Champernowne_constant.svg/100px-Champernowne_constant.svg.png) |
![{\displaystyle C_{10}}](//wikimedia.org/api/rest_v1/media/math/render/svg/8f0bd8c553212621651cc076b2b7043b87bb2182) |
![{\displaystyle \sum _{n=1}^{\infty }\;\sum _{k=10^{n-1}}^{10^{n}-1}{\frac {k}{10^{kn-9\sum _{j=0}^{n-1}10^{j}(n-j-1)}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/d2fe0a8afbe0e865064f7081393bc0fb3451f9e0) |
|
T |
ਫਰਮਾ:OEIS2C |
[0;8,9,1,149083,1,1,1,4,1,1,1,3,4,1,1,1,15,...] |
1933 |
0.12345678910111213141516171819202123 |
0.76422 36535 89220 66299[Mw 158] |
Landau-Ramanujan constant[183] |
|
![{\displaystyle K}](//wikimedia.org/api/rest_v1/media/math/render/svg/2b76fce82a62ed5461908f0dc8f037de4e3686b0) |
![{\displaystyle {\frac {1}{\sqrt {2}}}\prod _{p\equiv 3\!\!\!\!\!\mod \!4}\!\!{\underset {\!\!\!\!\!\!\!\!p:{\text{ prime}}}{\left(1-{\frac {1}{p^{2}}}\right)^{-{\frac {1}{2}}}}}\!\!={\frac {\pi }{4}}\prod _{p\equiv 1\!\!\!\!\!\mod \!4}\!\!{\underset {\!\!\!\!p:{\text{ prime}}}{\left(1-{\frac {1}{p^{2}}}\right)^{\frac {1}{2}}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/3a2a34dac776c4c939a866ecc3738cb8d541e4b9) |
|
T ? |
ਫਰਮਾ:OEIS2C |
[0;1,3,4,6,1,15,1,2,2,3,1,23,3,1,1,3,1,1,6,4,...] |
|
0.76422365358922066299069873125009232 |
2.71828 18284 59045 23536[Mw 159] |
Number e, Euler's number[184] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Exp_derivative_at_0.svg/100px-Exp_derivative_at_0.svg.png) |
![{\displaystyle {e}}](//wikimedia.org/api/rest_v1/media/math/render/svg/15bb27445ffb5a18fbf8e7fb86f498e4adaa0299) |
![{\displaystyle \!\lim _{n\to \infty }\!\left(\!1\!+\!{\frac {1}{n}}\right)^{n}\!=\!\sum _{n=0}^{\infty }{\frac {1}{n!}}={\frac {1}{0!}}+{\frac {1}{1}}+{\frac {1}{2!}}+{\frac {1}{3!}}+\textstyle \cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/71d8bdb3b234cfc9d23162c6cf870e66dd1c0f97) |
Sum[n=0 to ∞]
{1/n!}
(* lim_(n->∞)
(1+1/n)^n *)
|
T |
ਫਰਮਾ:OEIS2C |
[2;1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1,...] = [2;1,2p,1], p∈ℕ |
|
2.71828182845904523536028747135266250 |
0.36787 94411 71442 32159[Mw 160] |
Inverse of Number e[185] |
|
![{\displaystyle {\frac {1}{e}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/530c3934f29faf821bb239630994048bd45b1004) |
|
Sum[n=2 to ∞]
{(-1)^n/n!}
|
T |
ਫਰਮਾ:OEIS2C |
[0;2,1,1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,...] = [0;2,1,1,2p,1], p∈ℕ |
1618 |
0.36787944117144232159552377016146086 |
0.69034 71261 14964 31946 |
Upper iterated exponential[186] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/TetrationConvergence2D.png/100px-TetrationConvergence2D.png) |
![{\displaystyle {H}_{2n+1}}](//wikimedia.org/api/rest_v1/media/math/render/svg/c054c2803d348e8f8fea6d901dd5128e41200598) |
![{\displaystyle \lim _{n\to \infty }{H}_{2n+1}=\textstyle \left({\frac {1}{2}}\right)^{\left({\frac {1}{3}}\right)^{\left({\frac {1}{4}}\right)^{\cdot ^{\cdot ^{\left({\frac {1}{2n+1}}\right)}}}}}={2}^{-3^{-4^{\cdot ^{\cdot ^{-2n-1}}}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/3a59e15ff2082f5aefc7080afa1d478929a0bd61) |
2^-3^-4^-5^-6^
-7^-8^-9^-10^
-11^-12^-13 …
|
|
ਫਰਮਾ:OEIS2C |
[0;1,2,4,2,1,3,1,2,2,1,4,1,2,4,3,1,1,10,1,3,2,...] |
|
0.69034712611496431946732843846418942 |
0.65836 55992 ... |
Lower límit iterated exponential[187] |
| ![{\displaystyle {H}_{2n}}](//wikimedia.org/api/rest_v1/media/math/render/svg/59ec0c7f696d48354b17fb4621b8f54392e92e5e) |
![{\displaystyle \lim _{n\to \infty }{H}_{2n}=\textstyle \left({\frac {1}{2}}\right)^{\left({\frac {1}{3}}\right)^{\left({\frac {1}{4}}\right)^{\cdot ^{\cdot ^{\left({\frac {1}{2n}}\right)}}}}}={2}^{-3^{-4^{\cdot ^{\cdot ^{-2n}}}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/59b8ee7aa5cd06d6805f49a1aceeebd71fc8cad1) |
2^-3^-4^-5^-6^
-7^-8^-9^-10^
-11^-12 …
|
|
|
[0;1,1,1,12,1,2,1,1,4,3,1,1,2,1,2,1,51,2,2,1,...] |
|
0.6583655992... |
3.14159 26535 89793 23846[Mw 161] |
π number, Archimedes number[188] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/7/71/Sine_cosine_one_period.svg/100px-Sine_cosine_one_period.svg.png) |
![{\displaystyle \pi }](//wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a) |
![{\displaystyle \lim _{n\to \infty }\,2^{n}\underbrace {\sqrt {2-{\sqrt {2+{\sqrt {2+\cdots +{\sqrt {2}}}}}}}} _{n}}](//wikimedia.org/api/rest_v1/media/math/render/svg/298f7c09a43597963dfbd46fcdc08ae0b8f87d7c) |
Sum[n=0 to ∞]
{(-1)^n 4/(2n+1)}
|
T |
ਫਰਮਾ:OEIS2C |
[3;7,15,1,292,1,1,1,2,1,3,1,14,2,1,1,2,2,2,...] |
|
3.14159265358979323846264338327950288 |
1.92878 00...[Mw 162] |
Wright constant[189] |
|
![{\displaystyle {\omega }}](//wikimedia.org/api/rest_v1/media/math/render/svg/f399e6ed072a56c1fb767535d2fdf49978b45c6e) |
![{\displaystyle \left\lfloor 2^{2^{2^{\cdot ^{\cdot ^{2^{\omega }}}}}}\!\right\rfloor \scriptstyle {\text{= primes:}}\displaystyle \left\lfloor 2^{\omega }\right\rfloor \scriptstyle {\text{=3,}}\displaystyle \left\lfloor 2^{2^{\omega }}\right\rfloor \scriptstyle {\text{=13,}}\displaystyle \left\lfloor 2^{2^{2^{\omega }}}\right\rfloor \scriptstyle =16381,\ldots }](//wikimedia.org/api/rest_v1/media/math/render/svg/2d723d3b3613f58b1b397ec5bee69131033b3c30) |
|
|
ਫਰਮਾ:OEIS2C |
[1; 1, 13, 24, 2, 1, 1, 3, 1, 1, 3] |
|
1.9287800... |
0.46364 76090 00806 11621 |
Machin–Gregory series[190] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Arctangent.svg/100px-Arctangent.svg.png) |
![{\displaystyle \arctan {\frac {1}{2}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/b918c48df8e029184559da5708c06eac5273a824) |
![{\displaystyle {\underset {{\text{For }}x=1/2\qquad \qquad }{\sum _{n=0}^{\infty }{\frac {(\!-1\!)^{n}\,x^{2n+1}}{2n+1}}={\frac {1}{2}}{-}{\frac {1}{3\!\cdot \!2^{3}}}{+}{\frac {1}{5\!\cdot \!2^{5}}}{-}{\frac {1}{7\!\cdot \!2^{7}}}{+}\cdots }}}](//wikimedia.org/api/rest_v1/media/math/render/svg/63682fa7772df4bdb3fe5829886ac1471669ebfa) |
Sum[n=0 to ∞]
{(-1)^n (1/2)^(2n+1)
/(2n+1)}
|
I |
ਫਰਮਾ:OEIS2C |
[0;2,6,2,1,1,1,6,1,2,1,1,2,10,1,2,1,2,1,1,1,...] |
|
0.46364760900080611621425623146121440 |
0.69777 46579 64007 98200[Mw 163] |
Continued fraction constant, Bessel function[191] |
|
![{\displaystyle {C}_{CF}}](//wikimedia.org/api/rest_v1/media/math/render/svg/85ce333edc942848c2578863a7922c468148dd69) |
|
(Sum [n=0 to ∞]
{n/(n!n!)}) /
(Sum [n=0 to ∞]
{1/(n!n!)})
|
I |
ਫਰਮਾ:OEIS2C |
[0;1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,...] = [0;p+1], p∈ℕ
|
|
0.69777465796400798200679059255175260 |
1.90216 05831 04[Mw 164] |
Brun 2 constant = Σ inverse of Twin primes[192] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/1/18/Bruns-constant.svg/100px-Bruns-constant.svg.png) |
![{\displaystyle {B}_{\,2}}](//wikimedia.org/api/rest_v1/media/math/render/svg/68518f8835fa963dad91a3547ff035f10bd4e171) |
![{\displaystyle \textstyle {\underset {p,\,p+2:{\text{ prime}}}{\sum ({\frac {1}{p}}+{\frac {1}{p+2}})}}=({\frac {1}{3}}\!+\!{\frac {1}{5}})+({\tfrac {1}{5}}\!+\!{\tfrac {1}{7}})+({\tfrac {1}{11}}\!+\!{\tfrac {1}{13}})+\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/221c5fb68263e59d620bd8f60f75ace31178ffbf) |
|
|
ਫਰਮਾ:OEIS2C |
[1; 1, 9, 4, 1, 1, 8, 3, 4, 4, 2, 2] |
|
1.902160583104 |
0.87058 83799 75[Mw 165] |
Brun 4 constant = Σ inv.prime quadruplets[193] |
|
![{\displaystyle {B}_{\,4}}](//wikimedia.org/api/rest_v1/media/math/render/svg/8820c18969456105314fde5c106a508f411de952) |
![{\displaystyle \textstyle {\left({\tfrac {1}{5}}+{\tfrac {1}{7}}+{\tfrac {1}{11}}+{\tfrac {1}{13}}\right)}+\left({\tfrac {1}{11}}+{\tfrac {1}{13}}+{\tfrac {1}{17}}+{\tfrac {1}{19}}\right)+\dots }](//wikimedia.org/api/rest_v1/media/math/render/svg/b2c5cec9d79e37bb8c3b540454abb116b87cc762)
|
|
|
ਫਰਮਾ:OEIS2C |
[0; 1, 6, 1, 2, 1, 2, 956, 3, 1, 1] |
|
0.870588379975 |
0.63661 97723 67581 34307[Mw 166]
[Ow 8] |
Buffon constant[194] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Buffon2.png/100px-Buffon2.png) |
![{\displaystyle {\frac {2}{\pi }}}](//wikimedia.org/api/rest_v1/media/math/render/svg/61d9a566a0f4e1892e61f7140dacb7bed7f7b44e) |
Viète product |
|
T |
ਫਰਮਾ:OEIS2C |
[0;1,1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,...] |
1540 to 1603 |
0.63661977236758134307553505349005745 |
0.59634 73623 23194 07434[Mw 167] |
Euler–Gompertz constant[195] |
|
![{\displaystyle {G}}](//wikimedia.org/api/rest_v1/media/math/render/svg/f054c7208d06606d0d033b7ae5eb578bfb66aec3) |
|
integral[0 to ∞]
{(e^-n)/(1+n)}
|
I |
ਫਰਮਾ:OEIS2C |
[0;1,1,2,10,1,1,4,2,2,13,2,4,1,32,4,8,1,1,1,...]
|
|
0.59634736232319407434107849936927937 |
i ···[Mw 168] |
Imaginary number[196] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Complex_numbers_imaginary_unit.svg/100px-Complex_numbers_imaginary_unit.svg.png) |
![{\displaystyle {i}}](//wikimedia.org/api/rest_v1/media/math/render/svg/a51a9f4406a3037984ff353c247eb5731fc36cd9) |
![{\displaystyle {\sqrt {-1}}={\frac {\ln(-1)}{\pi }}\qquad \qquad \mathrm {e} ^{i\,\pi }=-1}](//wikimedia.org/api/rest_v1/media/math/render/svg/6626bf7414de7c7305b36e6754b02ddfa03b247e) |
|
C I |
|
|
1501 to 1576 |
i |
2.74723 82749 32304 33305 |
Ramanujan nested radical[197] |
|
![{\displaystyle R_{5}}](//wikimedia.org/api/rest_v1/media/math/render/svg/e4a18879dca7e62ef35d2bd35dd96747df96199d) |
![{\displaystyle \scriptstyle {\sqrt {5+{\sqrt {5+{\sqrt {5-{\sqrt {5+{\sqrt {5+{\sqrt {5+{\sqrt {5-\cdots }}}}}}}}}}}}}}\;=\textstyle {\frac {2+{\sqrt {5}}+{\sqrt {15-6{\sqrt {5}}}}}{2}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/f92b0855f237386a1cb3306ab97ff97092d4224f) |
(2+sqrt(5)
+sqrt(15
-6 sqrt(5)))/2
|
A |
|
[2;1,2,1,21,1,7,2,1,1,2,1,2,1,17,4,4,1,1,4,2,...] |
|
2.74723827493230433305746518613420282 |
0.56714 32904 09783 87299[Mw 169] |
Omega constant, Lambert W function[198] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Lambert-w.svg/100px-Lambert-w.svg.png) |
![{\displaystyle {\Omega }}](//wikimedia.org/api/rest_v1/media/math/render/svg/07b31b6e1a22be69e3dd0652027d20fb06a01789) |
![{\displaystyle \sum _{n=1}^{\infty }{\frac {(-n)^{n-1}}{n!}}=\,\left({\frac {1}{e}}\right)^{\left({\frac {1}{e}}\right)^{\cdot ^{\cdot ^{\left({\frac {1}{e}}\right)}}}}=e^{-\Omega }=e^{-e^{-e^{\cdot ^{\cdot ^{-e}}}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/a0dc7f1d7ee78048149394bf6fc3174e0a3740df) |
Sum[n=1 to ∞]
{(-n)^(n-1)/n!}
|
T |
ਫਰਮਾ:OEIS2C |
[0;1,1,3,4,2,10,4,1,1,1,1,2,7,306,1,5,1,2,1,...] |
|
0.56714329040978387299996866221035555 |
0.96894 61462 59369 38048 |
Beta(3)[199] |
|
![{\displaystyle {\beta }(3)}](//wikimedia.org/api/rest_v1/media/math/render/svg/0c72a6140390cb7ed9c977cef911fde7e6eaf06e) |
![{\displaystyle {\frac {\pi ^{3}}{32}}=\sum _{n=1}^{\infty }{\frac {-1^{n+1}}{(-1+2n)^{3}}}={\frac {1}{1^{3}}}{-}{\frac {1}{3^{3}}}{+}{\frac {1}{5^{3}}}{-}{\frac {1}{7^{3}}}{+}\cdots }](//wikimedia.org/api/rest_v1/media/math/render/svg/981fb6a8b5c05912ba97ea56bc73c9094c13275b) |
Sum[n=1 to ∞]
{(-1)^(n+1)
/(-1+2n)^3}
|
T |
ਫਰਮਾ:OEIS2C |
[0;1,31,4,1,18,21,1,1,2,1,2,1,3,6,3,28,1,...] |
|
0.96894614625936938048363484584691860 |
2.23606 79774 99789 69640 |
Square root of 5, Gauss sum[200] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/9/97/Pinwheel_1.svg/100px-Pinwheel_1.svg.png) |
![{\displaystyle {\sqrt {5}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/2b78ccdb7e18e02d4fc567c66aac99bf524acb5f) |
![{\displaystyle \scriptstyle (n=5)\displaystyle \sum _{k=0}^{n-1}e^{\frac {2k^{2}\pi i}{n}}=1+e^{\frac {2\pi i}{5}}+e^{\frac {8\pi i}{5}}+e^{\frac {18\pi i}{5}}+e^{\frac {32\pi i}{5}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/94a4813c06f3c37a6cba9c98e27889666731f685) |
Sum[k=0 to 4]
{e^(2k^2 pi i/5)}
|
A |
ਫਰਮਾ:OEIS2C |
[2;4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,...] = [2;4,...] |
|
2.23606797749978969640917366873127624 |
3.35988 56662 43177 55317[Mw 170] |
Prévost constant Reciprocal Fibonacci constant[201] |
|
![{\displaystyle \Psi }](//wikimedia.org/api/rest_v1/media/math/render/svg/f5471531a3fe80741a839bc98d49fae862a6439a) |
Fn: Fibonacci series |
Sum[n=1 to ∞]
{1/Fibonacci[n]}
|
I |
ਫਰਮਾ:OEIS2C |
[3;2,1,3,1,1,13,2,3,3,2,1,1,6,3,2,4,362,...] |
? |
3.35988566624317755317201130291892717 |
2.68545 20010 65306 44530[Mw 171] |
Khinchin's constant[202] |
![Thumb](//upload.wikimedia.org/wikipedia/commons/thumb/8/86/KhinchinBeispiele.svg/100px-KhinchinBeispiele.svg.png) |
![{\displaystyle K_{\,0}}](//wikimedia.org/api/rest_v1/media/math/render/svg/0a3ee0f4074c337bd9eedb2455fc1aa28e292076) |
![{\displaystyle \prod _{n=1}^{\infty }\left[{1+{1 \over n(n+2)}}\right]^{\ln n/\ln 2}}](//wikimedia.org/api/rest_v1/media/math/render/svg/cbfef25fcd2817842f1c50956dc798248c418be6) |
Prod[n=1 to ∞]
{(1+1/(n(n+2)))
^(ln(n)/ln(2))}
|
T |
ਫਰਮਾ:OEIS2C |
[2;1,2,5,1,1,2,1,1,3,10,2,1,3,2,24,1,3,2,...] |
1934 |
2.68545200106530644530971483548179569 |