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Statements
∫
0
∞
e
2
i
h
cosh
z
cosh
t
sinh
z
sinh
t
Fe
m
(
t
,
h
2
)
d
t
=
-
π
4
h
i
m
fe
m
′
(
0
,
h
2
)
Mc
m
(
3
)
(
z
,
h
)
,
superscript
subscript
0
superscript
𝑒
2
imaginary-unit
ℎ
𝑧
𝑡
𝑧
𝑡
modified-Mathieu-Fe
𝑚
𝑡
superscript
ℎ
2
𝑡
𝜋
4
ℎ
imaginary-unit
𝑚
diffop
Mathieu-fe
𝑚
1
0
superscript
ℎ
2
modified-Mathieu-Mc
3
𝑚
𝑧
ℎ
{\displaystyle{\displaystyle\int_{0}^{\infty}e^{2\mathrm{i}h\cosh z\cosh t}%
\sinh z\sinh t\mathrm{Fe}_{m}\left(t,h^{2}\right)\mathrm{d}t=-\dfrac{\pi}{4h}{%
\mathrm{i}^{m}}\mathrm{fe}_{m}'\left(0,h^{2}\right){\mathrm{Mc}^{(3)}_{m}}%
\left(z,h\right),}}
fe
n
(
z
,
q
)
Mathieu-fe
𝑛
𝑧
𝑞
{\displaystyle{\displaystyle\mathrm{fe}_{\NVar{n}}\left(\NVar{z},\NVar{q}%
\right)}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
cosh
z
𝑧
{\displaystyle{\displaystyle\cosh\NVar{z}}}
sinh
z
𝑧
{\displaystyle{\displaystyle\sinh\NVar{z}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
Fe
n
(
z
,
q
)
modified-Mathieu-Fe
𝑛
𝑧
𝑞
{\displaystyle{\displaystyle\mathrm{Fe}_{\NVar{n}}\left(\NVar{z},\NVar{q}%
\right)}}
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}}
z
𝑧
{\displaystyle{\displaystyle z}}
Identifiers
