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Statements
F
2
3
(
a
,
1
-
a
,
c
d
,
2
c
-
d
+
1
;
1
)
=
π
Γ
(
d
)
Γ
(
2
c
-
d
+
1
)
2
1
-
2
c
Γ
(
c
+
1
2
(
a
-
d
+
1
)
)
Γ
(
c
+
1
-
1
2
(
a
+
d
)
)
Γ
(
1
2
(
a
+
d
)
)
Γ
(
1
2
(
d
-
a
+
1
)
)
,
Gauss-hypergeometric-pFq
3
2
𝑎
1
𝑎
𝑐
𝑑
2
𝑐
𝑑
1
1
𝜋
Euler-Gamma
𝑑
Euler-Gamma
2
𝑐
𝑑
1
superscript
2
1
2
𝑐
Euler-Gamma
𝑐
1
2
𝑎
𝑑
1
Euler-Gamma
𝑐
1
1
2
𝑎
𝑑
Euler-Gamma
1
2
𝑎
𝑑
Euler-Gamma
1
2
𝑑
𝑎
1
{\displaystyle{\displaystyle{{}_{3}F_{2}}\left({a,1-a,c\atop d,2c-d+1};1\right%
)=\frac{\pi\Gamma\left(d\right)\Gamma\left(2c-d+1\right)2^{1-2c}}{\Gamma\left(%
c+\frac{1}{2}(a-d+1)\right)\Gamma\left(c+1-\frac{1}{2}(a+d)\right)\Gamma\left(%
\frac{1}{2}(a+d)\right)\Gamma\left(\frac{1}{2}(d-a+1)\right)},}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
F
q
p
(
a
1
,
…
,
a
p
;
b
1
,
…
,
b
q
;
z
)
Gauss-hypergeometric-pFq
𝑝
𝑞
subscript
𝑎
1
…
subscript
𝑎
𝑝
subscript
𝑏
1
…
subscript
𝑏
𝑞
𝑧
{\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots%
,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
a
,
a
1
,
…
,
a
p
𝑎
subscript
𝑎
1
…
subscript
𝑎
𝑝
{\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}
Identifiers
