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Statements
U
(
a
,
b
,
z
)
Γ
(
c
)
Γ
(
c
-
b
+
1
)
=
z
1
-
c
2
π
i
∫
-
∞
(
0
+
)
e
z
t
t
-
c
𝐅
1
2
(
a
,
c
;
a
+
c
-
b
+
1
;
1
-
1
t
)
d
t
,
Kummer-confluent-hypergeometric-U
𝑎
𝑏
𝑧
Euler-Gamma
𝑐
Euler-Gamma
𝑐
𝑏
1
superscript
𝑧
1
𝑐
2
𝜋
imaginary-unit
superscript
subscript
limit-from
0
superscript
𝑒
𝑧
𝑡
superscript
𝑡
𝑐
hypergeometric-bold-pFq
2
1
𝑎
𝑐
𝑎
𝑐
𝑏
1
1
1
𝑡
𝑡
{\displaystyle{\displaystyle\frac{U\left(a,b,z\right)}{\Gamma\left(c\right)%
\Gamma\left(c-b+1\right)}=\frac{z^{1-c}}{2\pi\mathrm{i}}\int_{-\infty}^{(0+)}e%
^{zt}t^{-c}{{}_{2}{\mathbf{F}}_{1}}\left(a,c;a+c-b+1;1-\frac{1}{t}\right)%
\mathrm{d}t,}}
|
ph
z
|
<
1
2
π
phase
𝑧
1
2
𝜋
{\displaystyle{\displaystyle\left|\operatorname{ph}z\right|<\frac{1}{2}\pi}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
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}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
z
𝑧
{\displaystyle{\displaystyle z}}
Identifiers
