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Statements
1
2
π
∫
ℒ
1
e
2
i
h
w
me
ν
(
t
,
h
2
)
d
t
=
e
i
ν
π
/
2
me
ν
(
α
,
h
2
)
M
ν
(
1
)
(
z
,
h
)
.
1
2
𝜋
subscript
subscript
ℒ
1
superscript
𝑒
2
imaginary-unit
ℎ
𝑤
Mathieu-me
𝜈
𝑡
superscript
ℎ
2
𝑡
superscript
𝑒
imaginary-unit
𝜈
𝜋
2
Mathieu-me
𝜈
𝛼
superscript
ℎ
2
modified-Mathieu-M
1
𝜈
𝑧
ℎ
{\displaystyle{\displaystyle\dfrac{1}{2\pi}\int_{\mathcal{L}_{1}}e^{2\mathrm{i%
}hw}\mathrm{me}_{\nu}\left(t,h^{2}\right)\mathrm{d}t=e^{\mathrm{i}\nu\pi/{2}}%
\mathrm{me}_{\nu}\left(\alpha,h^{2}\right){\mathrm{M}^{(1)}_{\nu}}\left(z,h%
\right).}}
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}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
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}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
w
(
z
)
𝑤
𝑧
{\displaystyle{\displaystyle w(z)}}
α
𝛼
{\displaystyle{\displaystyle\alpha}}
ℒ
j
subscript
ℒ
𝑗
{\displaystyle{\displaystyle\mathcal{L}_{j}}}
