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Statements
γ
ν
,
m
=
1
2
π
∫
0
2
π
me
ν
′
(
t
)
me
-
ν
-
2
m
(
t
)
d
t
=
(
-
1
)
m
4
i
π
me
ν
′
(
0
)
me
-
ν
-
2
m
(
0
)
D
1
(
ν
,
ν
+
2
m
,
0
)
.
subscript
𝛾
𝜈
𝑚
1
2
𝜋
superscript
subscript
0
2
𝜋
diffop
Mathieu-me
𝜈
1
𝑡
ℎ
Mathieu-me
𝜈
2
𝑚
𝑡
ℎ
𝑡
superscript
1
𝑚
4
imaginary-unit
𝜋
diffop
Mathieu-me
𝜈
1
0
ℎ
Mathieu-me
𝜈
2
𝑚
0
ℎ
Mathieu-D
1
𝜈
𝜈
2
𝑚
0
{\displaystyle{\displaystyle\gamma_{\nu,m}=\dfrac{1}{2\pi}\int_{0}^{2\pi}%
\mathrm{me}_{\nu}'\left(t\right)\mathrm{me}_{-\nu-2m}\left(t\right)\mathrm{d}t%
=(-1)^{m}\dfrac{4\mathrm{i}}{\pi}\frac{\mathrm{me}_{\nu}'\left(0\right)\mathrm%
{me}_{-\nu-2m}\left(0\right)}{\mathrm{D}_{1}\left(\nu,\nu+2m,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}}
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}}
Identifiers
