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Statements
M
ν
(
3
,
4
)
(
z
,
h
)
∼
e
±
i
(
2
h
cosh
z
-
(
1
2
ν
+
1
4
)
π
)
(
π
h
(
cosh
z
+
1
)
)
1
2
∑
m
=
0
∞
D
m
±
(
∓
4
i
h
(
cosh
z
+
1
)
)
m
,
asymptotic-expansion
modified-Mathieu-M
3
4
𝜈
𝑧
ℎ
superscript
𝑒
plus-or-minus
imaginary-unit
2
ℎ
𝑧
1
2
𝜈
1
4
𝜋
superscript
𝜋
ℎ
𝑧
1
1
2
superscript
subscript
𝑚
0
subscript
superscript
𝐷
plus-or-minus
𝑚
superscript
minus-or-plus
4
imaginary-unit
ℎ
𝑧
1
𝑚
{\displaystyle{\displaystyle{\mathrm{M}^{(3,4)}_{\nu}}\left(z,h\right)\sim%
\frac{e^{\pm\mathrm{i}\left(2h\cosh z-\left(\frac{1}{2}\nu+\frac{1}{4}\right)%
\pi\right)}}{\left(\pi h(\cosh z+1)\right)^{\frac{1}{2}}}\*\sum_{m=0}^{\infty}%
\dfrac{D^{\pm}_{m}}{\left(\mp 4\mathrm{i}h(\cosh z+1)\right)^{m}},}}
∼
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
cosh
z
𝑧
{\displaystyle{\displaystyle\cosh\NVar{z}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
M
ν
(
j
)
(
z
,
h
)
modified-Mathieu-M
𝑗
𝜈
𝑧
ℎ
{\displaystyle{\displaystyle{\mathrm{M}^{(\NVar{j})}_{\NVar{\nu}}}\left(\NVar{%
z},\NVar{h}\right)}}
m
𝑚
{\displaystyle{\displaystyle m}}
h
ℎ
{\displaystyle{\displaystyle h}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
D
m
±
superscript
subscript
𝐷
𝑚
plus-or-minus
{\displaystyle{\displaystyle D_{m}^{\pm}}}
Identifiers
