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Statements
Mc
2
m
(
j
)
(
z
,
h
)
=
(
-
1
)
m
(
ce
2
m
(
0
,
h
2
)
)
-
1
∑
ℓ
=
0
∞
(
-
1
)
ℓ
A
2
ℓ
2
m
(
h
2
)
𝒞
2
ℓ
(
j
)
(
2
h
cosh
z
)
,
modified-Mathieu-Mc
𝑗
2
𝑚
𝑧
ℎ
superscript
1
𝑚
superscript
Mathieu-ce
2
𝑚
0
superscript
ℎ
2
1
superscript
subscript
ℓ
0
superscript
1
ℓ
superscript
subscript
𝐴
2
ℓ
2
𝑚
superscript
ℎ
2
superscript
subscript
𝒞
2
ℓ
𝑗
2
ℎ
𝑧
{\displaystyle{\displaystyle{\mathrm{Mc}^{(j)}_{2m}}\left(z,h\right)=(-1)^{m}%
\left(\mathrm{ce}_{2m}\left(0,h^{2}\right)\right)^{-1}\sum_{\ell=0}^{\infty}(-%
1)^{\ell}A_{2\ell}^{2m}(h^{2}){\cal C}_{2\ell}^{(j)}(2h\cosh z),}}
ce
n
(
z
,
q
)
Mathieu-ce
𝑛
𝑧
𝑞
{\displaystyle{\displaystyle\mathrm{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}%
\right)}}
cosh
z
𝑧
{\displaystyle{\displaystyle\cosh\NVar{z}}}
Mc
n
(
j
)
(
z
,
h
)
modified-Mathieu-Mc
𝑗
𝑛
𝑧
ℎ
{\displaystyle{\displaystyle{\mathrm{Mc}^{(\NVar{j})}_{\NVar{n}}}\left(\NVar{z%
},\NVar{h}\right)}}
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)}}}
A
m
(
q
)
subscript
𝐴
𝑚
𝑞
{\displaystyle{\displaystyle A_{m}(q)}}
