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Statements
Γ
(
a
,
z
)
=
-
z
a
-
1
e
-
z
Γ
(
1
-
a
)
1
2
π
i
∫
c
-
i
∞
c
+
i
∞
Γ
(
s
+
1
-
a
)
π
z
-
s
sin
(
π
s
)
d
s
,
incomplete-Gamma
𝑎
𝑧
superscript
𝑧
𝑎
1
superscript
𝑒
𝑧
Euler-Gamma
1
𝑎
1
2
𝜋
𝑖
superscript
subscript
𝑐
𝑖
𝑐
𝑖
Euler-Gamma
𝑠
1
𝑎
𝜋
superscript
𝑧
𝑠
𝜋
𝑠
𝑠
{\displaystyle{\displaystyle\Gamma\left(a,z\right)=-\frac{z^{a-1}e^{-z}}{%
\Gamma\left(1-a\right)}\*\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\Gamma%
\left(s+1-a\right)\frac{\pi z^{-s}}{\sin\left(\pi s\right)}\mathrm{d}s,}}
|
ph
z
|
<
3
2
π
phase
𝑧
3
2
𝜋
{\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{3}{2}\pi}}
|
ph
z
|
<
3
2
π
ph
𝑧
3
2
𝜋
{\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{3}{2}\pi}}
a
≠
1
,
2
,
3
,
…
𝑎
1
2
3
…
{\displaystyle{\displaystyle a\neq 1,2,3,\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}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
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}}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
z
𝑧
{\displaystyle{\displaystyle z}}
a
𝑎
{\displaystyle{\displaystyle a}}
c
𝑐
{\displaystyle{\displaystyle c}}
Identifiers
