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Statements
∫
0
1
t
σ
-
1
(
1
-
t
)
c
-
1
R
-
a
(
b
1
,
b
2
;
t
,
1
)
d
t
=
Γ
(
c
)
Γ
(
σ
)
Γ
(
σ
+
b
2
-
a
)
Γ
(
σ
+
c
-
a
)
Γ
(
σ
+
b
2
)
,
superscript
subscript
0
1
superscript
𝑡
𝜎
1
superscript
1
𝑡
𝑐
1
Carlson-integral-R
𝑎
subscript
𝑏
1
subscript
𝑏
2
𝑡
1
𝑡
Euler-Gamma
𝑐
Euler-Gamma
𝜎
Euler-Gamma
𝜎
subscript
𝑏
2
𝑎
Euler-Gamma
𝜎
𝑐
𝑎
Euler-Gamma
𝜎
subscript
𝑏
2
{\displaystyle{\displaystyle\int_{0}^{1}t^{\sigma-1}(1-t)^{c-1}R_{-a}\left(b_{%
1},b_{2};t,1\right)\mathrm{d}t=\frac{\Gamma\left(c\right)\Gamma\left(\sigma%
\right)\Gamma\left(\sigma+b_{2}-a\right)}{\Gamma\left(\sigma+c-a\right)\Gamma%
\left(\sigma+b_{2}\right)},}}
ℜ
σ
>
max
(
0
,
a
-
b
2
)
𝜎
0
𝑎
subscript
𝑏
2
{\displaystyle{\displaystyle\Re\sigma>\max(0,a-b_{2})}}
c
=
b
1
+
b
2
>
0
𝑐
subscript
𝑏
1
subscript
𝑏
2
0
{\displaystyle{\displaystyle c=b_{1}+b_{2}>0}}
ℜ
σ
>
max
(
0
,
a
-
b
2
)
𝜎
0
𝑎
subscript
𝑏
2
{\displaystyle{\displaystyle\Re\sigma>\max(0,a-b_{2})}}
R
-
a
(
b
1
,
…
,
b
n
;
z
1
,
…
,
z
n
)
Carlson-integral-R
𝑎
subscript
𝑏
1
…
subscript
𝑏
𝑛
subscript
𝑧
1
…
subscript
𝑧
𝑛
{\displaystyle{\displaystyle R_{\NVar{-a}}\left(\NVar{b_{1}},\dots,\NVar{b_{n}%
};\NVar{z_{1}},\dots,\NVar{z_{n}}\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}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
σ
𝜎
{\displaystyle{\displaystyle\sigma}}
