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