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Statements
cosh
z
π
2
∫
0
2
π
sin
t
se
n
(
t
,
h
2
)
ce
m
(
t
,
h
2
)
sinh
2
z
+
sin
2
t
d
t
=
(
-
1
)
p
+
1
i
h
β
^
n
,
m
Dsc
0
(
n
,
m
,
z
)
,
𝑧
superscript
𝜋
2
superscript
subscript
0
2
𝜋
𝑡
Mathieu-se
𝑛
𝑡
superscript
ℎ
2
Mathieu-ce
𝑚
𝑡
superscript
ℎ
2
2
𝑧
2
𝑡
𝑡
superscript
1
𝑝
1
imaginary-unit
ℎ
subscript
^
𝛽
𝑛
𝑚
Mathieu-Dsc
0
𝑛
𝑚
𝑧
{\displaystyle{\displaystyle\dfrac{\cosh z}{\pi^{2}}\int_{0}^{2\pi}\dfrac{\sin
t%
\mathrm{se}_{n}\left(t,h^{2}\right)\mathrm{ce}_{m}\left(t,h^{2}\right)}{{\sinh%
^{2}}z+{\sin^{2}}t}\mathrm{d}t=(-1)^{p+1}\mathrm{i}h\widehat{\beta}_{n,m}%
\mathrm{Dsc}_{0}\left(n,m,z\right),}}
Dsc
j
(
n
,
m
,
z
)
Mathieu-Dsc
𝑗
𝑛
𝑚
𝑧
{\displaystyle{\displaystyle\mathrm{Dsc}_{\NVar{j}}\left(\NVar{n},\NVar{m},%
\NVar{z}\right)}}
ce
n
(
z
,
q
)
Mathieu-ce
𝑛
𝑧
𝑞
{\displaystyle{\displaystyle\mathrm{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}%
\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}}}
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}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
m
𝑚
{\displaystyle{\displaystyle m}}
h
ℎ
{\displaystyle{\displaystyle h}}
n
𝑛
{\displaystyle{\displaystyle n}}
z
𝑧
{\displaystyle{\displaystyle z}}
β
^
n
,
m
subscript
^
𝛽
𝑛
𝑚
{\displaystyle{\displaystyle\widehat{\beta}_{n,m}}}
