数学常数 (以连分数表示排列)

这是以连分数表示排列的数学常数列表。

(无理数的常数有无限长的连分数：其最后面项为...。)

符号	数集	值	连分数表示
Λ		> – 2.7 · 10−9
0	${\displaystyle \mathbb {N} }$	= 0	[0;]
M1		≈ 0.26149 72128 47642 78375 54268 38608 69585	[0; 3, 1, 4, 1, 2, 5, 2, 1, 1, 1, 1, 13, 4, 2, 4, 2, 1, 33, 296, 2, 1, 5, 19, 1, 5, 1, 1, 1, 1, 1]
½	${\displaystyle \mathbb {Q} }$	= 0.5	[0; 1, 1]
Ω 或 W(1)	${\displaystyle \mathbb {R} }$	≈ 0.56714 32904 09783 87299 99686 62210 35555	[0; 1, 1, 3, 4, 2, 10, 4, 1, 1, 1, 1, 2, 7, 306, 1, 5, 1, 2, 1, 5, 1, 1, 1, 1, 7, 1, 4, 2, ...]
γ		≈ 0.57721 56649 01532 86060 65120 90082 40243	[0; 1, 1, 2, 1, 2, 1, 4, 3, 13, 5, 1, 1, 8, 1, 2, 4, 1, 1, 40, 1, 11, 3, 7, 1, 7, 1, 1, 5, 1, 49, ...]
${\displaystyle \phi ^{-1}}$	${\displaystyle \mathbb {R} \backslash \mathbb {Q} }$	≈ 0.61803 39887	[0; 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …]
C2		≈ 0.66016 18158 46869 57392 78121 10014 55577	[0; 1, 1, 1, 16, 2, 2, 2, 2, 1, 18, 2, 2, 11, 1, 1, 2, 4, 1, 16, 3, 2, 4, 21, 2, 405, 2, 1, 33, 1, 1]
β*		≈ 0.70258	[0; 1, 2, 2, 1, 3, 5, 1, 2, 6, 1, 1, 5]
K	${\displaystyle \mathbb {R} \backslash \mathbb {Q} }$?	≈ 0.76422 36535 89220 66	[0; 1, 3, 4, 6, 1, 15, 1, 2, 2, 3, 1, 23, 3, 1, 1, 3, 1, 1, 7, 2, 3, 3, 18, 2, 1, 2, 1, 2, 1, 6]
B4		≈ 0.87058 83800	[0; 1, 6, 1, 2, 1, 2, 956, 8, 1, 1, 1, 23]
K		≈ 0.91596 55941 77219 01505 46035 14932 38411	[0; 1, 10, 1, 8, 1, 88, 4, 1, 1, 7, 22, 1, 2, 3, 26, 1, 11, 1, 10, 1, 9, 3, 1, 1, 1, 1, 1, 1, 2, 2]
1	${\displaystyle \mathbb {N} }$	= 1	[1;]
B´L		≈ 1.08366 （历史上的猜测值，实际值为1）	[1; 11, 1, 20, 2, 1, 12, 2, 2]
K		≈ 1.13198 824	[1; 7, 1, 1, 2, 1, 3, 2, 1, 2, 1, 17, 1, 1, 2, 1, 2, 4, 1, 2]
ρ	${\displaystyle \mathbb {R} }$	≈ 1.32471 95724 47460 25960 90885 44780 97340	[1; 1, 3, 12, 1, 1, 3, 2, 3, 2, 4, 2, 141, 80, 2, 5, 1, 2, 8, 2, 1, 1, 3, 1, 8, 2, 1, 1, 14, 1, 1, 2, 1, 1, 1, 3, 1, 10, 4 ...]
√2	${\displaystyle \mathbb {R} \backslash \mathbb {Q} }$	≈ 1.41421 35623 73095 04880 16887 24209 69807	[1; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ...]
μ		≈ 1.45136 92348 83381 05028 39684 85892 027	[1; 2, 4, 1, 1, 1, 3, 1, 1, 1, 2, 47, 2, 4, 1, 12, 1, 1, 2, 2, 1, 7, 2, 1, 1, 1, 2, 30, 6, 3, 6]
EB	${\displaystyle \mathbb {R} }$	≈ 1.60669 51524 15291 763	[1; 1, 1, 1, 1, 5, 2, 1, 2, 29, 4, 1, 2, 2, 2, 2, 6, 1, 7, 1, 6, 2, 1, 1, 1, 20, 1, 3, 1, 1, 1, ...]
φ	${\displaystyle \mathbb {R} \backslash \mathbb {Q} }$	≈ 1.61803 39887 49894 84820 45868 34365 63811	[1; 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...]
B2		≈ 1.90216 05823	[1; 1, 9, 4, 1, 1, 8, 3, 4, 7, 1, 3, 3, 1, 2, 1, 1, 12, 4, 2, 1, 2, 2]
2	${\displaystyle \mathbb {N} }$	= 2	[2;]
α		≈ 2.50290 78750 95892 82228 39028 73218 21578	[2; 1, 1, 85, 2, 8, 1, 10, 16, 3, 8, 9, 2, 1, 40, 1, 2, 3, 2, 2, 1, 17, 1, 1, 5, 3, 2, 6, 3, 5, 1]
e	${\displaystyle \mathbb {R} }$	≈ 2.71828 18284 59045 23536 02874 71352 66249	[2; 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, 1, 1, 10, 1, 1, 12, 1, 1, 14, 1, 1, 16, 1, 1, 18, 1, 1, 20, 1, ...]
K0		≈ 2.68545 20011 19507 41674	[2; 1, 2, 5, 1, 1, 2, 1, 1, 3, 10, 2, 1, 3, 2, 24, 1, 3, 2, 3, 1, 1, 1, 90]
3	${\displaystyle \mathbb {N} }$	= 3	[3;]
π	${\displaystyle \mathbb {R} }$	≈ 3.14159 26535 89793 23846 26433 83279 50288	[3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, 84, 2, 1, 1, 15, 3, 13, 1, 4, 2, ...]
4	${\displaystyle \mathbb {N} }$	= 4	[4;]
δ		≈ 4.66920 16091 02990 67185 32038 20466 20161	[4; 1, 2, 43, 2, 163, 2, 3, 1, 1, 2, 5, 1, 2, 3, 80, 2, 5, 2, 1, 1, 1, 33, 1, 1, 53, 1, 1, 1, 1, 1]

另见

• 数学常数