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Statements
1
2
π
i
∫
c
-
i
∞
c
+
i
∞
Γ
(
s
+
a
)
Γ
(
b
-
s
)
z
-
s
d
s
=
Γ
(
a
+
b
)
z
a
(
1
+
z
)
a
+
b
,
1
2
𝜋
𝑖
superscript
subscript
𝑐
𝑖
𝑐
𝑖
Euler-Gamma
𝑠
𝑎
Euler-Gamma
𝑏
𝑠
superscript
𝑧
𝑠
𝑠
Euler-Gamma
𝑎
𝑏
superscript
𝑧
𝑎
superscript
1
𝑧
𝑎
𝑏
{\displaystyle{\displaystyle{\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}%
\Gamma\left(s+a\right)\Gamma\left(b-s\right)z^{-s}\mathrm{d}s=\frac{\Gamma%
\left(a+b\right)z^{a}}{(1+z)^{a+b}}},}}
ℜ
(
a
+
b
)
>
0
𝑎
𝑏
0
{\displaystyle{\displaystyle\Re(a+b)>0}}
-
ℜ
a
<
c
<
ℜ
b
𝑎
𝑐
𝑏
{\displaystyle{\displaystyle-\Re a<c<\Re b}}
|
ph
z
|
<
π
phase
𝑧
𝜋
{\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}
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}}}
∫
{\displaystyle{\displaystyle\int}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
s
𝑠
{\displaystyle{\displaystyle s}}
z
𝑧
{\displaystyle{\displaystyle z}}
a
𝑎
{\displaystyle{\displaystyle a}}
b
𝑏
{\displaystyle{\displaystyle b}}
Identifiers
