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Statements
∫
-
∞
∞
d
t
Γ
(
a
+
t
)
Γ
(
b
+
t
)
Γ
(
c
-
t
)
Γ
(
d
-
t
)
=
Γ
(
a
+
b
+
c
+
d
-
3
)
Γ
(
a
+
c
-
1
)
Γ
(
a
+
d
-
1
)
Γ
(
b
+
c
-
1
)
Γ
(
b
+
d
-
1
)
,
superscript
subscript
𝑡
Euler-Gamma
𝑎
𝑡
Euler-Gamma
𝑏
𝑡
Euler-Gamma
𝑐
𝑡
Euler-Gamma
𝑑
𝑡
Euler-Gamma
𝑎
𝑏
𝑐
𝑑
3
Euler-Gamma
𝑎
𝑐
1
Euler-Gamma
𝑎
𝑑
1
Euler-Gamma
𝑏
𝑐
1
Euler-Gamma
𝑏
𝑑
1
{\displaystyle{\displaystyle\int_{-\infty}^{\infty}\frac{\mathrm{d}t}{\Gamma%
\left(a+t\right)\Gamma\left(b+t\right)\Gamma\left(c-t\right)\Gamma\left(d-t%
\right)}=\frac{\Gamma\left(a+b+c+d-3\right)}{\Gamma\left(a+c-1\right)\Gamma%
\left(a+d-1\right)\Gamma\left(b+c-1\right)\Gamma\left(b+d-1\right)},}}
ℜ
(
a
+
b
+
c
+
d
)
>
3
𝑎
𝑏
𝑐
𝑑
3
{\displaystyle{\displaystyle\Re(a+b+c+d)>3}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
∫
{\displaystyle{\displaystyle\int}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
a
𝑎
{\displaystyle{\displaystyle a}}
b
𝑏
{\displaystyle{\displaystyle b}}
Identifiers
