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Statements
2
π
2
∫
0
2
π
cos
t
sin
t
me
ν
(
t
,
h
2
)
me
-
ν
-
2
m
(
t
,
h
2
)
sinh
2
z
+
sin
2
t
d
t
=
(
-
1
)
m
i
γ
ν
,
m
D
0
(
ν
,
ν
+
2
m
,
z
)
,
2
superscript
𝜋
2
superscript
subscript
0
2
𝜋
𝑡
𝑡
Mathieu-me
𝜈
𝑡
superscript
ℎ
2
Mathieu-me
𝜈
2
𝑚
𝑡
superscript
ℎ
2
2
𝑧
2
𝑡
𝑡
superscript
1
𝑚
imaginary-unit
subscript
𝛾
𝜈
𝑚
Mathieu-D
0
𝜈
𝜈
2
𝑚
𝑧
{\displaystyle{\displaystyle\dfrac{2}{\pi^{2}}\int_{0}^{2\pi}\dfrac{\cos t\sin
t%
\mathrm{me}_{\nu}\left(t,h^{2}\right)\mathrm{me}_{-\nu-2m}\left(t,h^{2}\right)%
}{{\sinh^{2}}z+{\sin^{2}}t}\mathrm{d}t=(-1)^{m}\mathrm{i}\gamma_{\nu,m}\mathrm%
{D}_{0}\left(\nu,\nu+2m,z\right),}}
D
j
(
ν
,
μ
,
z
)
Mathieu-D
𝑗
𝜈
𝜇
𝑧
{\displaystyle{\displaystyle\mathrm{D}_{\NVar{j}}\left(\NVar{\nu},\NVar{\mu},%
\NVar{z}\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}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
sinh
z
𝑧
{\displaystyle{\displaystyle\sinh\NVar{z}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
m
𝑚
{\displaystyle{\displaystyle m}}
h
ℎ
{\displaystyle{\displaystyle h}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
γ
ν
,
m
subscript
𝛾
𝜈
𝑚
{\displaystyle{\displaystyle\gamma_{\nu,m}}}
Identifiers
