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Statements
(
a
-
d
)
(
b
-
d
)
(
c
-
d
)
(
F
2
3
(
a
,
b
,
c
d
+
1
,
e
;
1
)
-
F
2
3
(
a
,
b
,
c
d
,
e
;
1
)
)
+
a
b
c
F
2
3
(
a
,
b
,
c
d
,
e
;
1
)
=
d
(
d
-
1
)
(
a
+
b
+
c
-
d
-
e
+
1
)
(
F
2
3
(
a
,
b
,
c
d
,
e
;
1
)
-
F
2
3
(
a
,
b
,
c
d
-
1
,
e
;
1
)
)
,
𝑎
𝑑
𝑏
𝑑
𝑐
𝑑
Gauss-hypergeometric-pFq
3
2
𝑎
𝑏
𝑐
𝑑
1
𝑒
1
Gauss-hypergeometric-pFq
3
2
𝑎
𝑏
𝑐
𝑑
𝑒
1
𝑎
𝑏
𝑐
Gauss-hypergeometric-pFq
3
2
𝑎
𝑏
𝑐
𝑑
𝑒
1
𝑑
𝑑
1
𝑎
𝑏
𝑐
𝑑
𝑒
1
Gauss-hypergeometric-pFq
3
2
𝑎
𝑏
𝑐
𝑑
𝑒
1
Gauss-hypergeometric-pFq
3
2
𝑎
𝑏
𝑐
𝑑
1
𝑒
1
{\displaystyle{\displaystyle(a-d)(b-d)(c-d)\left({{}_{3}F_{2}}\left({a,b,c%
\atop d+1,e};1\right)-{{}_{3}F_{2}}\left({a,b,c\atop d,e};1\right)\right)+abc{%
{}_{3}F_{2}}\left({a,b,c\atop d,e};1\right)=d(d-1)(a+b+c-d-e+1)\left({{}_{3}F_%
{2}}\left({a,b,c\atop d,e};1\right)-{{}_{3}F_{2}}\left({a,b,c\atop d-1,e};1%
\right)\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
{\displaystyle{\displaystyle a}}
b
𝑏
{\displaystyle{\displaystyle b}}
c
𝑐
{\displaystyle{\displaystyle c}}
d
𝑑
{\displaystyle{\displaystyle d}}
e
𝑒
{\displaystyle{\displaystyle e}}
Identifiers
