Coshc
(
z
)
=
(
i
z
+
1
/
2
π
)
M
(
1
,
2
,
i
π
−
2
z
)
e
1
/
2
i
π
−
z
z
{\displaystyle \operatorname {Coshc} (z)={\frac {\left(iz+1/2\,\pi \right){{\rm {M}}\left(1,\,2,\,i\pi -2\,z\right)}}{{{\rm {e}}^{1/2\,i\pi -z}}z}}}
Coshc
(
z
)
=
1
2
(
2
i
z
+
π
)
H
e
u
n
B
(
2
,
0
,
0
,
0
,
2
1
/
2
i
π
−
z
)
e
1
/
2
i
π
−
z
z
{\displaystyle \operatorname {Coshc} (z)={\frac {1}{2}}\,{\frac {\left(2\,iz+\pi \right){\it {HeunB}}\left(2,0,0,0,{\sqrt {2}}{\sqrt {1/2\,i\pi -z}}\right)}{{{\rm {e}}^{1/2\,i\pi -z}}z}}}
Coshc
(
z
)
=
−
i
(
2
i
z
+
π
)
W
h
i
t
t
a
k
e
r
M
(
0
,
1
/
2
,
i
π
−
2
z
)
(
4
i
z
+
2
π
)
z
{\displaystyle \operatorname {Coshc} (z)={\frac {-i\left(2\,iz+\pi \right){{\rm {\mathbf {W} hittakerM}}\left(0,\,1/2,\,i\pi -2\,z\right)}}{\left(4\,iz+2\,\pi \right)z}}}
Coshc
z
≈
(
z
−
1
+
1
2
z
+
1
24
z
3
+
1
720
z
5
+
1
40320
z
7
+
1
3628800
z
9
+
1
479001600
z
11
+
1
87178291200
z
13
+
O
(
z
15
)
)
{\displaystyle \operatorname {Coshc} z\approx ({z}^{-1}+{\frac {1}{2}}z+{\frac {1}{24}}{z}^{3}+{\frac {1}{720}}{z}^{5}+{\frac {1}{40320}}{z}^{7}+{\frac {1}{3628800}}{z}^{9}+{\frac {1}{479001600}}{z}^{11}+{\frac {1}{87178291200}}{z}^{13}+O\left({z}^{15}\right))}
Coshc abs complex 3D
Coshc Im complex 3D plot
Coshc Re complex 3D plot
Coshc'(z) Im complex 3D plot
Coshc'(z) Re complex 3D plot
Coshc'(z) abs complex 3D plot
Coshc'(x) abs density plot
Coshc'(x) Im density plot
Coshc'(x) Re density plot
PN Den Outer, TM Nieuwenhuizen, A Lagendijk,Location of objects in multiple-scattering media,JOSA A, Vol. 10, Issue 6, pp. 1209-1218 (1993)
T Körpinar ,New characterizations for minimizing energy of biharmonic particles in Heisenberg spacetime - International Journal of Theoretical Physics, 2014 - Springer
Nilg¨un S¨onmez,A Trigonometric Proof of the Euler Theorem in Hyperbolic Geometry,International Mathematical Forum, 4, 2009, no. 38, 1877 - 1881
JHM ten Thije Boonkkamp, J van Dijk, L Liu,Extension of the complete flux scheme to systems of conservation laws,J Sci Comput (2012) 53:552–568,DOI 10.1007/s10915-012-9588-5