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