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:8.6.E6 - MaRDI portal
Statements
Γ
(
a
,
z
)
=
2
z
1
2
a
e
-
z
Γ
(
1
-
a
)
∫
0
∞
e
-
t
t
-
1
2
a
K
a
(
2
z
t
)
d
t
,
incomplete-Gamma
𝑎
𝑧
2
superscript
𝑧
1
2
𝑎
superscript
𝑒
𝑧
Euler-Gamma
1
𝑎
superscript
subscript
0
superscript
𝑒
𝑡
superscript
𝑡
1
2
𝑎
modified-Bessel-second-kind
𝑎
2
𝑧
𝑡
𝑡
{\displaystyle{\displaystyle\Gamma\left(a,z\right)=\frac{2z^{\frac{1}{2}a}e^{-%
z}}{\Gamma\left(1-a\right)}\int_{0}^{\infty}e^{-t}t^{-\frac{1}{2}a}K_{a}\left(%
2\sqrt{zt}\right)\mathrm{d}t,}}
ℜ
a
<
1
𝑎
1
{\displaystyle{\displaystyle\Re a<1}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
Γ
(
a
,
z
)
incomplete-Gamma
𝑎
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}
∫
{\displaystyle{\displaystyle\int}}
K
ν
(
z
)
modified-Bessel-second-kind
𝜈
𝑧
{\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
z
𝑧
{\displaystyle{\displaystyle z}}
a
𝑎
{\displaystyle{\displaystyle a}}
