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:14.20.E22 - MaRDI portal
Statements
𝖯
-
1
2
+
i
τ
-
μ
(
x
)
=
β
exp
(
μ
β
arctan
β
)
Γ
(
μ
+
1
)
(
1
+
β
2
)
μ
/
2
e
-
μ
ρ
(
1
+
β
2
-
x
2
β
2
)
1
/
4
(
1
+
O
(
1
μ
)
)
,
Ferrers-Legendre-P-first-kind
𝜇
1
2
𝑖
𝜏
𝑥
𝛽
𝜇
𝛽
𝛽
Euler-Gamma
𝜇
1
superscript
1
superscript
𝛽
2
𝜇
2
superscript
𝑒
𝜇
𝜌
superscript
1
superscript
𝛽
2
superscript
𝑥
2
superscript
𝛽
2
1
4
1
Big-O
1
𝜇
{\displaystyle{\displaystyle\mathsf{P}^{-\mu}_{-\frac{1}{2}+i\tau}\left(x%
\right)=\frac{\beta\exp\left(\mu\beta\operatorname{arctan}\beta\right)}{\Gamma%
\left(\mu+1\right)\left(1+\beta^{2}\right)^{\mu/2}}\frac{e^{-\mu\rho}}{\left(1%
+\beta^{2}-x^{2}\beta^{2}\right)^{1/4}}\left(1+O\left(\frac{1}{\mu}\right)%
\right),}}
O
(
x
)
Big-O
𝑥
{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
𝖯
ν
μ
(
x
)
Ferrers-Legendre-P-first-kind
𝜇
𝜈
𝑥
{\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}%
\right)}}
exp
z
𝑧
{\displaystyle{\displaystyle\exp\NVar{z}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
arctan
z
𝑧
{\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}
x
𝑥
{\displaystyle{\displaystyle x}}
τ
𝜏
{\displaystyle{\displaystyle\tau}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
β
𝛽
{\displaystyle{\displaystyle\beta}}
ρ
𝜌
{\displaystyle{\displaystyle\rho}}
