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:13.4.E8 - MaRDI portal
Statements
U
(
a
,
b
,
z
)
=
z
c
-
a
∫
0
∞
e
-
z
t
t
c
-
1
𝐅
1
2
(
a
,
a
-
b
+
1
;
c
;
-
t
)
d
t
,
Kummer-confluent-hypergeometric-U
𝑎
𝑏
𝑧
superscript
𝑧
𝑐
𝑎
superscript
subscript
0
superscript
𝑒
𝑧
𝑡
superscript
𝑡
𝑐
1
hypergeometric-bold-pFq
2
1
𝑎
𝑎
𝑏
1
𝑐
𝑡
𝑡
{\displaystyle{\displaystyle U\left(a,b,z\right)=z^{c-a}\*\int_{0}^{\infty}e^{%
-zt}t^{c-1}{{}_{2}{\mathbf{F}}_{1}}\left(a,a-b+1;c;-t\right)\mathrm{d}t,}}
|
ph
z
|
<
1
2
π
phase
𝑧
1
2
𝜋
{\displaystyle{\displaystyle|\operatorname{ph}{z}|<\frac{1}{2}\pi}}
U
(
a
,
b
,
z
)
Kummer-confluent-hypergeometric-U
𝑎
𝑏
𝑧
{\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
𝐅
q
p
(
𝐚
;
𝐛
;
)
hypergeometric-bold-pFq
𝑝
𝑞
𝐚
𝐛
{\displaystyle{\displaystyle{{}_{\NVar{p}}{\mathbf{F}}_{\NVar{q}}}\left(\NVar{%
\mathbf{a}};\NVar{\mathbf{b}};\right)\)\@add@PDF@RDFa@triples\end{document}}}
∫
{\displaystyle{\displaystyle\int}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
z
𝑧
{\displaystyle{\displaystyle z}}
c
𝑐
{\displaystyle{\displaystyle c}}
