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Statements
U
(
a
,
b
,
z
)
=
e
-
a
π
i
Γ
(
1
-
a
)
2
π
i
∫
∞
(
0
+
)
e
-
z
t
t
a
-
1
(
1
+
t
)
b
-
a
-
1
d
t
,
Kummer-confluent-hypergeometric-U
𝑎
𝑏
𝑧
superscript
𝑒
𝑎
𝜋
imaginary-unit
Euler-Gamma
1
𝑎
2
𝜋
imaginary-unit
superscript
subscript
limit-from
0
superscript
𝑒
𝑧
𝑡
superscript
𝑡
𝑎
1
superscript
1
𝑡
𝑏
𝑎
1
𝑡
{\displaystyle{\displaystyle U\left(a,b,z\right)=e^{-a\pi\mathrm{i}}\frac{%
\Gamma\left(1-a\right)}{2\pi\mathrm{i}}\int_{\infty}^{(0+)}e^{-zt}t^{a-1}{(1+t%
)^{b-a-1}}\mathrm{d}t,}}
|
ph
z
|
<
1
2
π
phase
𝑧
1
2
𝜋
{\displaystyle{\displaystyle\left|\operatorname{ph}z\right|<\frac{1}{2}\pi}}
a
≠
1
,
2
,
3
,
…
𝑎
1
2
3
…
{\displaystyle{\displaystyle a\neq 1,2,3,\dots}}
|
ph
z
|
<
1
2
π
ph
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}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
z
𝑧
{\displaystyle{\displaystyle z}}
Identifiers
