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:10.27.E11 - MaRDI portal
Statements
Y
ν
(
z
)
=
e
±
(
ν
+
1
)
π
i
/
2
I
ν
(
z
e
∓
π
i
/
2
)
-
(
2
/
π
)
e
∓
ν
π
i
/
2
K
ν
(
z
e
∓
π
i
/
2
)
,
Bessel-Y-Weber
𝜈
𝑧
superscript
𝑒
plus-or-minus
𝜈
1
𝜋
𝑖
2
modified-Bessel-first-kind
𝜈
𝑧
superscript
𝑒
minus-or-plus
𝜋
𝑖
2
2
𝜋
superscript
𝑒
minus-or-plus
𝜈
𝜋
𝑖
2
modified-Bessel-second-kind
𝜈
𝑧
superscript
𝑒
minus-or-plus
𝜋
𝑖
2
{\displaystyle{\displaystyle Y_{\nu}\left(z\right)=e^{\pm(\nu+1)\pi i/2}I_{\nu%
}\left(ze^{\mp\pi i/2}\right)-(2/\pi)e^{\mp\nu\pi i/2}K_{\nu}\left(ze^{\mp\pi i%
/2}\right),}}
-
1
2
π
≤
±
ph
z
≤
π
1
2
𝜋
plus-or-minus
phase
𝑧
𝜋
{\displaystyle{\displaystyle-\tfrac{1}{2}\pi\leq\pm\operatorname{ph}z\leq\pi}}
Y
ν
(
z
)
Bessel-Y-Weber
𝜈
𝑧
{\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
I
ν
(
z
)
modified-Bessel-first-kind
𝜈
𝑧
{\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
K
ν
(
z
)
modified-Bessel-second-kind
𝜈
𝑧
{\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
