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:33.16.E12 - MaRDI portal
Statements
f
(
ϵ
,
ℓ
;
r
)
=
(
-
1
)
ℓ
ν
ℓ
+
1
π
(
-
π
ξ
ℓ
(
-
ν
,
r
)
Γ
(
ℓ
+
1
+
ν
)
+
sin
(
π
ν
)
cos
(
π
ν
)
Γ
(
ν
-
ℓ
)
ζ
ℓ
(
-
ν
,
r
)
)
,
Coulomb-f
italic-ϵ
ℓ
𝑟
superscript
1
ℓ
superscript
𝜈
ℓ
1
𝜋
𝜋
subscript
𝜉
ℓ
𝜈
𝑟
Euler-Gamma
ℓ
1
𝜈
𝜋
𝜈
𝜋
𝜈
Euler-Gamma
𝜈
ℓ
subscript
𝜁
ℓ
𝜈
𝑟
{\displaystyle{\displaystyle f\left(\epsilon,\ell;r\right)=\frac{(-1)^{\ell}%
\nu^{\ell+1}}{\pi}\left(-\frac{\pi\xi_{\ell}(-\nu,r)}{\Gamma\left(\ell+1+\nu%
\right)}+\sin\left(\pi\nu\right)\cos\left(\pi\nu\right)\Gamma\left(\nu-\ell%
\right)\zeta_{\ell}(-\nu,r)\right),}}
f
(
ϵ
,
ℓ
;
r
)
Coulomb-f
italic-ϵ
ℓ
𝑟
{\displaystyle{\displaystyle f\left(\NVar{\epsilon},\NVar{\ell};\NVar{r}\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}}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
ℓ
ℓ
{\displaystyle{\displaystyle\ell}}
r
𝑟
{\displaystyle{\displaystyle r}}
ϵ
italic-ϵ
{\displaystyle{\displaystyle\epsilon}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
ζ
ℓ
(
ν
,
r
)
subscript
𝜁
ℓ
𝜈
𝑟
{\displaystyle{\displaystyle\zeta_{\ell}(\nu,r)}}
ξ
ℓ
(
ν
,
r
)
subscript
𝜉
ℓ
𝜈
𝑟
{\displaystyle{\displaystyle\xi_{\ell}(\nu,r)}}
Identifiers
