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Statements
me
ν
(
1
2
π
,
h
2
)
M
ν
(
j
)
(
z
,
h
)
=
e
i
ν
π
/
2
∑
n
=
-
∞
∞
c
2
n
ν
(
h
2
)
𝒞
ν
+
2
n
(
j
)
(
2
h
sinh
z
)
,
Mathieu-me
𝜈
1
2
𝜋
superscript
ℎ
2
modified-Mathieu-M
𝑗
𝜈
𝑧
ℎ
superscript
𝑒
imaginary-unit
𝜈
𝜋
2
superscript
subscript
𝑛
superscript
subscript
𝑐
2
𝑛
𝜈
superscript
ℎ
2
superscript
subscript
𝒞
𝜈
2
𝑛
𝑗
2
ℎ
𝑧
{\displaystyle{\displaystyle\mathrm{me}_{\nu}\left(\tfrac{1}{2}\pi,h^{2}\right%
){\mathrm{M}^{(j)}_{\nu}}\left(z,h\right)=e^{\mathrm{i}\nu\ifrac{\pi}{2}}\sum_%
{n=-\infty}^{\infty}c_{2n}^{\nu}(h^{2}){\cal C}_{\nu+2n}^{(j)}(2h\sinh z),}}
me
n
(
z
,
q
)
Mathieu-me
𝑛
𝑧
𝑞
{\displaystyle{\displaystyle\mathrm{me}_{\NVar{n}}\left(\NVar{z},\NVar{q}%
\right)}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
sinh
z
𝑧
{\displaystyle{\displaystyle\sinh\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)}}
h
ℎ
{\displaystyle{\displaystyle h}}
n
𝑛
{\displaystyle{\displaystyle n}}
j
𝑗
{\displaystyle{\displaystyle j}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
c
2
m
(
q
)
subscript
𝑐
2
𝑚
𝑞
{\displaystyle{\displaystyle c_{2m}(q)}}
𝒞
μ
(
j
)
superscript
subscript
𝒞
𝜇
𝑗
{\displaystyle{\displaystyle\mathcal{C}_{\mu}^{(j)}}}
