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Statements
Y
ν
(
z
)
=
2
(
1
2
z
)
ν
π
1
2
Γ
(
ν
+
1
2
)
(
∫
0
1
(
1
-
t
2
)
ν
-
1
2
sin
(
z
t
)
d
t
-
∫
0
∞
e
-
z
t
(
1
+
t
2
)
ν
-
1
2
d
t
)
,
Bessel-Y-Weber
𝜈
𝑧
2
superscript
1
2
𝑧
𝜈
superscript
𝜋
1
2
Euler-Gamma
𝜈
1
2
superscript
subscript
0
1
superscript
1
superscript
𝑡
2
𝜈
1
2
𝑧
𝑡
𝑡
superscript
subscript
0
superscript
𝑒
𝑧
𝑡
superscript
1
superscript
𝑡
2
𝜈
1
2
𝑡
{\displaystyle{\displaystyle Y_{\nu}\left(z\right)=\frac{2(\tfrac{1}{2}z)^{\nu%
}}{\pi^{\frac{1}{2}}\Gamma\left(\nu+\tfrac{1}{2}\right)}\left(\int_{0}^{1}(1-t%
^{2})^{\nu-\frac{1}{2}}\sin\left(zt\right)\mathrm{d}t-\int_{0}^{\infty}e^{-zt}%
(1+t^{2})^{\nu-\frac{1}{2}}\mathrm{d}t\right),}}
ℜ
ν
>
-
1
2
,
|
ph
z
|
<
1
2
π
formulae-sequence
𝜈
1
2
phase
𝑧
1
2
𝜋
{\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2},|\operatorname{ph}z|<\tfrac{1%
}{2}\pi}}
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}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
∫
{\displaystyle{\displaystyle\int}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
