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Statements
∑
n
=
-
∞
∞
Γ
(
a
+
n
)
Γ
(
b
+
n
)
Γ
(
c
+
n
)
Γ
(
d
+
n
)
=
π
2
sin
(
π
a
)
sin
(
π
b
)
Γ
(
c
+
d
-
a
-
b
-
1
)
Γ
(
c
-
a
)
Γ
(
d
-
a
)
Γ
(
c
-
b
)
Γ
(
d
-
b
)
.
superscript
subscript
𝑛
Euler-Gamma
𝑎
𝑛
Euler-Gamma
𝑏
𝑛
Euler-Gamma
𝑐
𝑛
Euler-Gamma
𝑑
𝑛
superscript
𝜋
2
𝜋
𝑎
𝜋
𝑏
Euler-Gamma
𝑐
𝑑
𝑎
𝑏
1
Euler-Gamma
𝑐
𝑎
Euler-Gamma
𝑑
𝑎
Euler-Gamma
𝑐
𝑏
Euler-Gamma
𝑑
𝑏
{\displaystyle{\displaystyle\sum_{n=-\infty}^{\infty}\frac{\Gamma\left(a+n%
\right)\Gamma\left(b+n\right)}{\Gamma\left(c+n\right)\Gamma\left(d+n\right)}=%
\frac{\pi^{2}}{\sin\left(\pi a\right)\sin\left(\pi b\right)}\*\frac{\Gamma%
\left(c+d-a-b-1\right)}{\Gamma\left(c-a\right)\Gamma\left(d-a\right)\Gamma%
\left(c-b\right)\Gamma\left(d-b\right)}.}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
n
𝑛
{\displaystyle{\displaystyle n}}
a
𝑎
{\displaystyle{\displaystyle a}}
b
𝑏
{\displaystyle{\displaystyle b}}
c
𝑐
{\displaystyle{\displaystyle c}}
Identifiers
