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