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Statements
Ms
2
m
+
2
(
j
)
(
z
,
h
)
=
(
-
1
)
m
(
se
2
m
+
2
′
(
0
,
h
2
)
)
-
1
tanh
z
∑
ℓ
=
0
∞
(
-
1
)
ℓ
(
2
ℓ
+
2
)
B
2
ℓ
+
2
2
m
+
2
(
h
2
)
𝒞
2
ℓ
+
2
(
j
)
(
2
h
cosh
z
)
,
modified-Mathieu-Ms
𝑗
2
𝑚
2
𝑧
ℎ
superscript
1
𝑚
superscript
diffop
Mathieu-se
2
𝑚
2
1
0
superscript
ℎ
2
1
𝑧
superscript
subscript
ℓ
0
superscript
1
ℓ
2
ℓ
2
superscript
subscript
𝐵
2
ℓ
2
2
𝑚
2
superscript
ℎ
2
superscript
subscript
𝒞
2
ℓ
2
𝑗
2
ℎ
𝑧
{\displaystyle{\displaystyle{\mathrm{Ms}^{(j)}_{2m+2}}\left(z,h\right)=(-1)^{m%
}\left(\mathrm{se}_{2m+2}'\left(0,h^{2}\right)\right)^{-1}\tanh z\sum_{\ell=0}%
^{\infty}(-1)^{\ell}(2\ell+2)B_{2\ell+2}^{2m+2}(h^{2}){\cal C}_{2\ell+2}^{(j)}%
(2h\cosh z),}}
se
n
(
z
,
q
)
Mathieu-se
𝑛
𝑧
𝑞
{\displaystyle{\displaystyle\mathrm{se}_{\NVar{n}}\left(\NVar{z},\NVar{q}%
\right)}}
cosh
z
𝑧
{\displaystyle{\displaystyle\cosh\NVar{z}}}
tanh
z
𝑧
{\displaystyle{\displaystyle\tanh\NVar{z}}}
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)}}
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)}}}
B
m
(
q
)
subscript
𝐵
𝑚
𝑞
{\displaystyle{\displaystyle B_{m}(q)}}
Identifiers
