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Statements
1
2
π
∫
0
2
π
e
2
i
h
w
se
n
(
t
,
h
2
)
d
t
=
i
n
se
n
(
α
,
h
2
)
Ms
n
(
1
)
(
z
,
h
)
,
1
2
𝜋
superscript
subscript
0
2
𝜋
superscript
𝑒
2
imaginary-unit
ℎ
𝑤
Mathieu-se
𝑛
𝑡
superscript
ℎ
2
𝑡
imaginary-unit
𝑛
Mathieu-se
𝑛
𝛼
superscript
ℎ
2
modified-Mathieu-Ms
1
𝑛
𝑧
ℎ
{\displaystyle{\displaystyle\dfrac{1}{2\pi}\int_{0}^{2\pi}e^{2\mathrm{i}hw}%
\mathrm{se}_{n}\left(t,h^{2}\right)\mathrm{d}t={\mathrm{i}^{n}}\mathrm{se}_{n}%
\left(\alpha,h^{2}\right){\mathrm{Ms}^{(1)}_{n}}\left(z,h\right),}}
se
n
(
z
,
q
)
Mathieu-se
𝑛
𝑧
𝑞
{\displaystyle{\displaystyle\mathrm{se}_{\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}}
Ms
n
(
j
)
(
z
,
h
)
modified-Mathieu-Ms
𝑗
𝑛
𝑧
ℎ
{\displaystyle{\displaystyle{\mathrm{Ms}^{(\NVar{j})}_{\NVar{n}}}\left(\NVar{z%
},\NVar{h}\right)}}
h
ℎ
{\displaystyle{\displaystyle h}}
n
𝑛
{\displaystyle{\displaystyle n}}
z
𝑧
{\displaystyle{\displaystyle z}}
w
(
z
)
𝑤
𝑧
{\displaystyle{\displaystyle w(z)}}
α
𝛼
{\displaystyle{\displaystyle\alpha}}
