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