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Statements
∫
V
n
(
1
-
∑
k
=
1
n
t
k
)
z
n
+
1
-
1
∏
k
=
1
n
t
k
z
k
-
1
d
t
k
=
Γ
(
z
1
)
Γ
(
z
2
)
⋯
Γ
(
z
n
+
1
)
Γ
(
z
1
+
z
2
+
…
+
z
n
+
1
)
.
subscript
subscript
𝑉
𝑛
superscript
1
superscript
subscript
𝑘
1
𝑛
subscript
𝑡
𝑘
subscript
𝑧
𝑛
1
1
superscript
subscript
product
𝑘
1
𝑛
superscript
subscript
𝑡
𝑘
subscript
𝑧
𝑘
1
subscript
𝑡
𝑘
Euler-Gamma
subscript
𝑧
1
Euler-Gamma
subscript
𝑧
2
⋯
Euler-Gamma
subscript
𝑧
𝑛
1
Euler-Gamma
subscript
𝑧
1
subscript
𝑧
2
…
subscript
𝑧
𝑛
1
{\displaystyle{\displaystyle\int_{V_{n}}\left(1-\sum_{k=1}^{n}t_{k}\right)^{z_%
{n+1}-1}\prod_{k=1}^{n}t_{k}^{z_{k}-1}\mathrm{d}t_{k}=\frac{\Gamma\left(z_{1}%
\right)\Gamma\left(z_{2}\right)\cdots\Gamma\left(z_{n+1}\right)}{\Gamma\left(z%
_{1}+z_{2}+\dots+z_{n+1}\right)}.}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
∫
{\displaystyle{\displaystyle\int}}
n
𝑛
{\displaystyle{\displaystyle n}}
k
𝑘
{\displaystyle{\displaystyle k}}
z
𝑧
{\displaystyle{\displaystyle z}}
V
n
subscript
𝑉
𝑛
{\displaystyle{\displaystyle V_{n}}}
