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Statements
∫
0
π
/
2
J
0
(
2
q
(
cos
2
τ
-
sin
2
ζ
)
)
ce
2
n
(
τ
,
q
)
d
τ
=
w
II
(
1
2
π
;
a
2
n
(
q
)
,
q
)
ce
2
n
(
ζ
,
q
)
,
superscript
subscript
0
𝜋
2
Bessel-J
0
2
𝑞
2
𝜏
2
𝜁
Mathieu-ce
2
𝑛
𝜏
𝑞
𝜏
subscript
𝑤
II
1
2
𝜋
Mathieu-eigenvalue-a
2
𝑛
𝑞
𝑞
Mathieu-ce
2
𝑛
𝜁
𝑞
{\displaystyle{\displaystyle\int_{0}^{\ifrac{\pi}{2}}J_{0}\left(2\sqrt{q({\cos%
^{2}}\tau-{\sin^{2}}\zeta)}\right)\mathrm{ce}_{2n}\left(\tau,q\right)\mathrm{d%
}\tau=w_{\mbox{\tiny II}}(\tfrac{1}{2}\pi;a_{2n}\left(q\right),q)\mathrm{ce}_{%
2n}\left(\zeta,q\right),}}
J
ν
(
z
)
Bessel-J
𝜈
𝑧
{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
ce
n
(
z
,
q
)
Mathieu-ce
𝑛
𝑧
𝑞
{\displaystyle{\displaystyle\mathrm{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}%
\right)}}
a
n
(
q
)
Mathieu-eigenvalue-a
𝑛
𝑞
{\displaystyle{\displaystyle a_{\NVar{n}}\left(\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}}}
q
=
h
2
𝑞
superscript
ℎ
2
{\displaystyle{\displaystyle q=h^{2}}}
n
𝑛
{\displaystyle{\displaystyle n}}
w
II
(
z
;
a
,
q
)
subscript
𝑤
II
𝑧
𝑎
𝑞
{\displaystyle{\displaystyle w_{\mbox{\tiny II}}(z;a,q)}}
