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DLMF:8.6.E10 - MaRDI portal
Statements
γ
(
a
,
z
)
=
1
2
π
i
∫
c
-
i
∞
c
+
i
∞
Γ
(
s
)
a
-
s
z
a
-
s
d
s
,
incomplete-gamma
𝑎
𝑧
1
2
𝜋
𝑖
superscript
subscript
𝑐
𝑖
𝑐
𝑖
Euler-Gamma
𝑠
𝑎
𝑠
superscript
𝑧
𝑎
𝑠
𝑠
{\displaystyle{\displaystyle\gamma\left(a,z\right)=\frac{1}{2\pi i}\int_{c-i%
\infty}^{c+i\infty}\frac{\Gamma\left(s\right)}{a-s}z^{a-s}\mathrm{d}s,}}
|
ph
z
|
<
1
2
π
phase
𝑧
1
2
𝜋
{\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{2}\pi}}
|
ph
z
|
<
1
2
π
ph
𝑧
1
2
𝜋
{\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{2}\pi}}
a
≠
0
,
-
1
,
-
2
,
…
𝑎
0
1
2
…
{\displaystyle{\displaystyle a\neq 0,-1,-2,\dots}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
γ
(
a
,
z
)
incomplete-gamma
𝑎
𝑧
{\displaystyle{\displaystyle\gamma\left(\NVar{a},\NVar{z}\right)}}
∫
{\displaystyle{\displaystyle\int}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
z
𝑧
{\displaystyle{\displaystyle z}}
a
𝑎
{\displaystyle{\displaystyle a}}
c
𝑐
{\displaystyle{\displaystyle c}}
Identifiers