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Statements
∫
0
1
2
π
J
μ
(
z
sin
θ
)
I
ν
(
z
cos
θ
)
(
tan
θ
)
μ
+
1
d
θ
=
Γ
(
1
2
ν
-
1
2
μ
)
(
1
2
z
)
μ
2
Γ
(
1
2
ν
+
1
2
μ
+
1
)
J
ν
(
z
)
,
superscript
subscript
0
1
2
𝜋
Bessel-J
𝜇
𝑧
𝜃
modified-Bessel-first-kind
𝜈
𝑧
𝜃
superscript
𝜃
𝜇
1
𝜃
Euler-Gamma
1
2
𝜈
1
2
𝜇
superscript
1
2
𝑧
𝜇
2
Euler-Gamma
1
2
𝜈
1
2
𝜇
1
Bessel-J
𝜈
𝑧
{\displaystyle{\displaystyle\int_{0}^{\frac{1}{2}\pi}J_{\mu}\left(z\sin\theta%
\right)I_{\nu}\left(z\cos\theta\right)(\tan\theta)^{\mu+1}\mathrm{d}\theta=%
\frac{\Gamma\left(\tfrac{1}{2}\nu-\tfrac{1}{2}\mu\right)(\tfrac{1}{2}z)^{\mu}}%
{2\Gamma\left(\tfrac{1}{2}\nu+\tfrac{1}{2}\mu+1\right)}J_{\nu}\left(z\right),}}
ℜ
ν
>
ℜ
μ
>
-
1
𝜈
𝜇
1
{\displaystyle{\displaystyle\Re\nu>\Re\mu>-1}}
J
ν
(
z
)
Bessel-J
𝜈
𝑧
{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
∫
{\displaystyle{\displaystyle\int}}
I
ν
(
z
)
modified-Bessel-first-kind
𝜈
𝑧
{\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
tan
z
𝑧
{\displaystyle{\displaystyle\tan\NVar{z}}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
