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