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Statements
2
π
∫
0
π
𝒞
2
ℓ
+
2
(
j
)
(
2
h
R
)
sin
(
(
2
ℓ
+
2
)
ϕ
)
se
2
m
+
2
(
t
,
h
2
)
d
t
=
(
-
1
)
ℓ
+
m
B
2
ℓ
+
2
2
m
+
2
(
h
2
)
Ms
2
m
+
2
(
j
)
(
z
,
h
)
.
2
𝜋
superscript
subscript
0
𝜋
subscript
superscript
𝒞
𝑗
2
ℓ
2
2
ℎ
𝑅
2
ℓ
2
italic-ϕ
Mathieu-se
2
𝑚
2
𝑡
superscript
ℎ
2
𝑡
superscript
1
ℓ
𝑚
subscript
superscript
𝐵
2
𝑚
2
2
ℓ
2
superscript
ℎ
2
modified-Mathieu-Ms
𝑗
2
𝑚
2
𝑧
ℎ
{\displaystyle{\displaystyle\dfrac{2}{\pi}\int_{0}^{\pi}\mathcal{C}^{(j)}_{2%
\ell+2}(2hR)\sin\left((2\ell+2)\phi\right)\mathrm{se}_{2m+2}\left(t,h^{2}%
\right)\mathrm{d}t=(-1)^{\ell+m}B^{2m+2}_{2\ell+2}(h^{2}){\mathrm{Ms}^{(j)}_{2%
m+2}}\left(z,h\right).}}
se
n
(
z
,
q
)
Mathieu-se
𝑛
𝑧
𝑞
{\displaystyle{\displaystyle\mathrm{se}_{\NVar{n}}\left(\NVar{z},\NVar{q}%
\right)}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
∫
{\displaystyle{\displaystyle\int}}
Ms
n
(
j
)
(
z
,
h
)
modified-Mathieu-Ms
𝑗
𝑛
𝑧
ℎ
{\displaystyle{\displaystyle{\mathrm{Ms}^{(\NVar{j})}_{\NVar{n}}}\left(\NVar{z%
},\NVar{h}\right)}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
m
𝑚
{\displaystyle{\displaystyle m}}
h
ℎ
{\displaystyle{\displaystyle h}}
j
𝑗
{\displaystyle{\displaystyle j}}
z
𝑧
{\displaystyle{\displaystyle z}}
𝒞
μ
(
j
)
superscript
subscript
𝒞
𝜇
𝑗
{\displaystyle{\displaystyle\mathcal{C}_{\mu}^{(j)}}}
ϕ
(
z
,
t
)
italic-ϕ
𝑧
𝑡
{\displaystyle{\displaystyle\phi(z,t)}}
R
(
z
,
t
)
𝑅
𝑧
𝑡
{\displaystyle{\displaystyle R(z,t)}}
B
m
(
q
)
subscript
𝐵
𝑚
𝑞
{\displaystyle{\displaystyle B_{m}(q)}}
