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Statements
∫
0
∞
e
-
z
t
t
b
-
1
U
(
a
,
c
,
t
)
d
t
=
Γ
(
b
)
Γ
(
b
-
c
+
1
)
z
-
b
𝐅
1
2
(
a
,
b
;
a
+
b
-
c
+
1
;
1
-
1
z
)
,
superscript
subscript
0
superscript
𝑒
𝑧
𝑡
superscript
𝑡
𝑏
1
Kummer-confluent-hypergeometric-U
𝑎
𝑐
𝑡
𝑡
Euler-Gamma
𝑏
Euler-Gamma
𝑏
𝑐
1
superscript
𝑧
𝑏
hypergeometric-bold-pFq
2
1
𝑎
𝑏
𝑎
𝑏
𝑐
1
1
1
𝑧
{\displaystyle{\displaystyle\int_{0}^{\infty}e^{-zt}t^{b-1}U\left(a,c,t\right)%
\mathrm{d}t=\Gamma\left(b\right)\Gamma\left(b-c+1\right)\*z^{-b}{{}_{2}{%
\mathbf{F}}_{1}}\left(a,b;a+b-c+1;1-\frac{1}{z}\right),}}
ℜ
b
>
max
(
ℜ
c
-
1
,
0
)
𝑏
𝑐
1
0
{\displaystyle{\displaystyle\Re b>\max\left(\Re c-1,0\right)}}
ℜ
z
>
0
𝑧
0
{\displaystyle{\displaystyle\Re z>0}}
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)}}
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}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
z
𝑧
{\displaystyle{\displaystyle z}}
Identifiers
