Deprecated : $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372 DLMF:10.9.E7 - MaRDI portal
Statements
Y
ν
(
z
)
=
1
π
∫
0
π
sin
(
z
sin
θ
-
ν
θ
)
d
θ
-
1
π
∫
0
∞
(
e
ν
t
+
e
-
ν
t
cos
(
ν
π
)
)
e
-
z
sinh
t
d
t
,
Bessel-Y-Weber
𝜈
𝑧
1
𝜋
superscript
subscript
0
𝜋
𝑧
𝜃
𝜈
𝜃
𝜃
1
𝜋
superscript
subscript
0
superscript
𝑒
𝜈
𝑡
superscript
𝑒
𝜈
𝑡
𝜈
𝜋
superscript
𝑒
𝑧
𝑡
𝑡
{\displaystyle{\displaystyle Y_{\nu}\left(z\right)=\frac{1}{\pi}\int_{0}^{\pi}%
\sin\left(z\sin\theta-\nu\theta\right)\mathrm{d}\theta-\frac{1}{\pi}\int_{0}^{%
\infty}\left(e^{\nu t}+e^{-\nu t}\cos\left(\nu\pi\right)\right)e^{-z\sinh t}%
\mathrm{d}t,}}
|
ph
z
|
<
1
2
π
phase
𝑧
1
2
𝜋
{\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{2}\pi}}
Y
ν
(
z
)
Bessel-Y-Weber
𝜈
𝑧
{\displaystyle{\displaystyle Y_{\NVar{\nu}}\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}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
sinh
z
𝑧
{\displaystyle{\displaystyle\sinh\NVar{z}}}
∫
{\displaystyle{\displaystyle\int}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
