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Statements
2
π
∫
0
π
/
2
sin
(
2
h
cos
z
cos
t
)
ce
2
n
+
1
(
t
,
h
2
)
d
t
=
-
h
A
1
2
n
+
1
(
h
2
)
ce
2
n
+
1
′
(
1
2
π
,
h
2
)
ce
2
n
+
1
(
z
,
h
2
)
,
2
𝜋
superscript
subscript
0
𝜋
2
2
ℎ
𝑧
𝑡
Mathieu-ce
2
𝑛
1
𝑡
superscript
ℎ
2
𝑡
ℎ
superscript
subscript
𝐴
1
2
𝑛
1
superscript
ℎ
2
diffop
Mathieu-ce
2
𝑛
1
1
1
2
𝜋
superscript
ℎ
2
Mathieu-ce
2
𝑛
1
𝑧
superscript
ℎ
2
{\displaystyle{\displaystyle\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\sin\left(2h%
\cos z\cos t\right)\mathrm{ce}_{2n+1}\left(t,h^{2}\right)\mathrm{d}t=-\frac{hA%
_{1}^{2n+1}(h^{2})}{\mathrm{ce}_{2n+1}'\left(\frac{1}{2}\pi,h^{2}\right)}%
\mathrm{ce}_{2n+1}\left(z,h^{2}\right),}}
ce
n
(
z
,
q
)
Mathieu-ce
𝑛
𝑧
𝑞
{\displaystyle{\displaystyle\mathrm{ce}_{\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}}}
∫
{\displaystyle{\displaystyle\int}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
h
ℎ
{\displaystyle{\displaystyle h}}
n
𝑛
{\displaystyle{\displaystyle n}}
z
𝑧
{\displaystyle{\displaystyle z}}
A
m
(
q
)
subscript
𝐴
𝑚
𝑞
{\displaystyle{\displaystyle A_{m}(q)}}
