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DLMF:28.31.E23 - MaRDI portal
Statements
∫
u
0
u
∞
∫
0
2
π
ℎ𝑠
p
1
m
1
(
u
,
ξ
)
ℎ𝑠
p
1
m
1
(
v
,
ξ
)
ℎ𝑠
p
2
m
2
(
u
,
ξ
)
ℎ𝑠
p
2
m
2
(
v
,
ξ
)
(
cos
(
2
u
)
-
cos
(
2
v
)
)
d
v
d
u
=
0
,
superscript
subscript
subscript
𝑢
0
subscript
𝑢
superscript
subscript
0
2
𝜋
superscript
subscript
ℎ𝑠
subscript
𝑝
1
subscript
𝑚
1
𝑢
𝜉
superscript
subscript
ℎ𝑠
subscript
𝑝
1
subscript
𝑚
1
𝑣
𝜉
superscript
subscript
ℎ𝑠
subscript
𝑝
2
subscript
𝑚
2
𝑢
𝜉
superscript
subscript
ℎ𝑠
subscript
𝑝
2
subscript
𝑚
2
𝑣
𝜉
2
𝑢
2
𝑣
𝑣
𝑢
0
{\displaystyle{\displaystyle\int_{u_{0}}^{u_{\infty}}\int_{0}^{2\pi}\mathit{hs%
}_{p_{1}}^{m_{1}}(u,\xi)\mathit{hs}_{p_{1}}^{m_{1}}(v,\xi)\mathit{hs}_{p_{2}}^%
{m_{2}}(u,\xi)\mathit{hs}_{p_{2}}^{m_{2}}(v,\xi)\*\left(\cos\left(2u\right)-%
\cos\left(2v\right)\right)\mathrm{d}v\mathrm{d}u=0,}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
∫
{\displaystyle{\displaystyle\int}}
m
𝑚
{\displaystyle{\displaystyle m}}
ℎ𝑠
p
m
(
z
,
ξ
)
superscript
subscript
ℎ𝑠
𝑝
𝑚
𝑧
𝜉
{\displaystyle{\displaystyle\mathit{hs}_{p}^{m}(z,\xi)}}
Identifiers