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Statements
∫
0
∞
t
μ
Y
ν
(
t
)
d
t
=
2
μ
π
Γ
(
1
2
μ
+
1
2
ν
+
1
2
)
Γ
(
1
2
μ
-
1
2
ν
+
1
2
)
sin
(
1
2
μ
-
1
2
ν
)
π
,
superscript
subscript
0
superscript
𝑡
𝜇
Bessel-Y-Weber
𝜈
𝑡
𝑡
superscript
2
𝜇
𝜋
Euler-Gamma
1
2
𝜇
1
2
𝜈
1
2
Euler-Gamma
1
2
𝜇
1
2
𝜈
1
2
1
2
𝜇
1
2
𝜈
𝜋
{\displaystyle{\displaystyle\int_{0}^{\infty}t^{\mu}Y_{\nu}\left(t\right)%
\mathrm{d}t=\frac{2^{\mu}}{\pi}\Gamma\left(\tfrac{1}{2}\mu+\tfrac{1}{2}\nu+%
\tfrac{1}{2}\right)\Gamma\left(\tfrac{1}{2}\mu-\tfrac{1}{2}\nu+\tfrac{1}{2}%
\right)\sin\left(\tfrac{1}{2}\mu-\tfrac{1}{2}\nu\right)\pi,}}
ℜ
(
μ
±
ν
)
>
-
1
plus-or-minus
𝜇
𝜈
1
{\displaystyle{\displaystyle\Re(\mu\pm\nu)>-1}}
ℜ
μ
<
1
2
𝜇
1
2
{\displaystyle{\displaystyle\Re\mu<\tfrac{1}{2}}}
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}}
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}}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
