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Statements
me
ν
′
(
0
,
h
2
)
M
ν
(
j
)
(
z
,
h
)
=
i
tanh
z
∑
n
=
-
∞
∞
(
-
1
)
n
(
ν
+
2
n
)
c
2
n
ν
(
h
2
)
𝒞
ν
+
2
n
(
j
)
(
2
h
cosh
z
)
,
diffop
Mathieu-me
𝜈
1
0
superscript
ℎ
2
modified-Mathieu-M
𝑗
𝜈
𝑧
ℎ
imaginary-unit
𝑧
superscript
subscript
𝑛
superscript
1
𝑛
𝜈
2
𝑛
superscript
subscript
𝑐
2
𝑛
𝜈
superscript
ℎ
2
superscript
subscript
𝒞
𝜈
2
𝑛
𝑗
2
ℎ
𝑧
{\displaystyle{\displaystyle\mathrm{me}_{\nu}'\left(0,h^{2}\right){\mathrm{M}^%
{(j)}_{\nu}}\left(z,h\right)=\mathrm{i}\tanh z\sum_{n=-\infty}^{\infty}(-1)^{n%
}(\nu+2n)c_{2n}^{\nu}(h^{2}){\cal C}_{\nu+2n}^{(j)}(2h\cosh z),}}
me
n
(
z
,
q
)
Mathieu-me
𝑛
𝑧
𝑞
{\displaystyle{\displaystyle\mathrm{me}_{\NVar{n}}\left(\NVar{z},\NVar{q}%
\right)}}
cosh
z
𝑧
{\displaystyle{\displaystyle\cosh\NVar{z}}}
tanh
z
𝑧
{\displaystyle{\displaystyle\tanh\NVar{z}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
M
ν
(
j
)
(
z
,
h
)
modified-Mathieu-M
𝑗
𝜈
𝑧
ℎ
{\displaystyle{\displaystyle{\mathrm{M}^{(\NVar{j})}_{\NVar{\nu}}}\left(\NVar{%
z},\NVar{h}\right)}}
h
ℎ
{\displaystyle{\displaystyle h}}
n
𝑛
{\displaystyle{\displaystyle n}}
j
𝑗
{\displaystyle{\displaystyle j}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
c
2
m
(
q
)
subscript
𝑐
2
𝑚
𝑞
{\displaystyle{\displaystyle c_{2m}(q)}}
𝒞
μ
(
j
)
superscript
subscript
𝒞
𝜇
𝑗
{\displaystyle{\displaystyle\mathcal{C}_{\mu}^{(j)}}}
Identifiers
