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Statements
α
ν
,
m
(
0
)
=
1
2
π
∫
0
2
π
cos
t
me
ν
(
t
,
h
2
)
me
-
ν
-
2
m
-
1
(
t
,
h
2
)
d
t
=
(
-
1
)
m
2
i
π
me
ν
(
0
,
h
2
)
me
-
ν
-
2
m
-
1
(
0
,
h
2
)
h
D
0
(
ν
,
ν
+
2
m
+
1
,
0
)
,
subscript
superscript
𝛼
0
𝜈
𝑚
1
2
𝜋
superscript
subscript
0
2
𝜋
𝑡
Mathieu-me
𝜈
𝑡
superscript
ℎ
2
Mathieu-me
𝜈
2
𝑚
1
𝑡
superscript
ℎ
2
𝑡
superscript
1
𝑚
2
imaginary-unit
𝜋
Mathieu-me
𝜈
0
superscript
ℎ
2
Mathieu-me
𝜈
2
𝑚
1
0
superscript
ℎ
2
ℎ
Mathieu-D
0
𝜈
𝜈
2
𝑚
1
0
{\displaystyle{\displaystyle\alpha^{(0)}_{\nu,m}=\dfrac{1}{2\pi}\int_{0}^{2\pi%
}\cos t\mathrm{me}_{\nu}\left(t,h^{2}\right)\mathrm{me}_{-\nu-2m-1}\left(t,h^{%
2}\right)\mathrm{d}t=(-1)^{m}\dfrac{2\mathrm{i}}{\pi}\dfrac{\mathrm{me}_{\nu}%
\left(0,h^{2}\right)\mathrm{me}_{-\nu-2m-1}\left(0,h^{2}\right)}{h\mathrm{D}_{%
0}\left(\nu,\nu+2m+1,0\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}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
m
𝑚
{\displaystyle{\displaystyle m}}
h
ℎ
{\displaystyle{\displaystyle h}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
