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Statements
U
(
a
,
b
,
z
)
=
1
Γ
(
a
)
∫
0
∞
e
-
z
t
t
a
-
1
(
1
+
t
)
b
-
a
-
1
d
t
,
Kummer-confluent-hypergeometric-U
𝑎
𝑏
𝑧
1
Euler-Gamma
𝑎
superscript
subscript
0
superscript
𝑒
𝑧
𝑡
superscript
𝑡
𝑎
1
superscript
1
𝑡
𝑏
𝑎
1
𝑡
{\displaystyle{\displaystyle U\left(a,b,z\right)=\frac{1}{\Gamma\left(a\right)%
}\int_{0}^{\infty}e^{-zt}t^{a-1}(1+t)^{b-a-1}\mathrm{d}t,}}
ℜ
a
>
0
𝑎
0
{\displaystyle{\displaystyle\Re a>0}}
|
ph
z
|
<
1
2
π
phase
𝑧
1
2
𝜋
{\displaystyle{\displaystyle|\operatorname{ph}{z}|<\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}}}
∫
{\displaystyle{\displaystyle\int}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
z
𝑧
{\displaystyle{\displaystyle z}}
