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Statements
α
^
n
,
m
(
c
)
=
1
2
π
∫
0
2
π
cos
t
ce
n
(
t
,
h
2
)
ce
m
(
t
,
h
2
)
d
t
=
(
-
1
)
p
+
1
2
i
π
ce
n
(
0
,
h
2
)
ce
m
(
0
,
h
2
)
h
Dc
0
(
n
,
m
,
0
)
.
superscript
subscript
^
𝛼
𝑛
𝑚
𝑐
1
2
𝜋
superscript
subscript
0
2
𝜋
𝑡
Mathieu-ce
𝑛
𝑡
superscript
ℎ
2
Mathieu-ce
𝑚
𝑡
superscript
ℎ
2
𝑡
superscript
1
𝑝
1
2
imaginary-unit
𝜋
Mathieu-ce
𝑛
0
superscript
ℎ
2
Mathieu-ce
𝑚
0
superscript
ℎ
2
ℎ
Mathieu-Dc
0
𝑛
𝑚
0
{\displaystyle{\displaystyle\widehat{\alpha}_{n,m}^{(c)}=\frac{1}{2\pi}\int_{0%
}^{2\pi}\cos t\mathrm{ce}_{n}\left(t,h^{2}\right)\mathrm{ce}_{m}\left(t,h^{2}%
\right)\mathrm{d}t=(-1)^{p+1}\dfrac{2}{\mathrm{i}\pi}\dfrac{\mathrm{ce}_{n}%
\left(0,h^{2}\right)\mathrm{ce}_{m}\left(0,h^{2}\right)}{h\mathrm{Dc}_{0}\left%
(n,m,0\right)}.}}
Dc
j
(
n
,
m
,
z
)
Mathieu-Dc
𝑗
𝑛
𝑚
𝑧
{\displaystyle{\displaystyle\mathrm{Dc}_{\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)}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
m
𝑚
{\displaystyle{\displaystyle m}}
h
ℎ
{\displaystyle{\displaystyle h}}
n
𝑛
{\displaystyle{\displaystyle n}}
Identifiers
