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Statements
F
6
7
(
a
,
1
2
a
+
1
,
b
,
c
,
d
,
f
,
-
n
1
2
a
,
a
-
b
+
1
,
a
-
c
+
1
,
a
-
d
+
1
,
a
-
f
+
1
,
a
+
n
+
1
;
1
)
=
(
a
+
1
)
n
(
a
-
b
-
c
+
1
)
n
(
a
-
b
-
d
+
1
)
n
(
a
-
c
-
d
+
1
)
n
(
a
-
b
+
1
)
n
(
a
-
c
+
1
)
n
(
a
-
d
+
1
)
n
(
a
-
b
-
c
-
d
+
1
)
n
,
Gauss-hypergeometric-pFq
7
6
𝑎
1
2
𝑎
1
𝑏
𝑐
𝑑
𝑓
𝑛
1
2
𝑎
𝑎
𝑏
1
𝑎
𝑐
1
𝑎
𝑑
1
𝑎
𝑓
1
𝑎
𝑛
1
1
Pochhammer
𝑎
1
𝑛
Pochhammer
𝑎
𝑏
𝑐
1
𝑛
Pochhammer
𝑎
𝑏
𝑑
1
𝑛
Pochhammer
𝑎
𝑐
𝑑
1
𝑛
Pochhammer
𝑎
𝑏
1
𝑛
Pochhammer
𝑎
𝑐
1
𝑛
Pochhammer
𝑎
𝑑
1
𝑛
Pochhammer
𝑎
𝑏
𝑐
𝑑
1
𝑛
{\displaystyle{\displaystyle{{}_{7}F_{6}}\left({a,\frac{1}{2}a+1,b,c,d,f,-n%
\atop\frac{1}{2}a,a-b+1,a-c+1,a-d+1,a-f+1,a+n+1};1\right)=\frac{{\left(a+1%
\right)_{n}}{\left(a-b-c+1\right)_{n}}{\left(a-b-d+1\right)_{n}}{\left(a-c-d+1%
\right)_{n}}}{{\left(a-b+1\right)_{n}}{\left(a-c+1\right)_{n}}{\left(a-d+1%
\right)_{n}}{\left(a-b-c-d+1\right)_{n}}},}}
n
=
0
,
1
,
…
𝑛
0
1
…
{\displaystyle{\displaystyle n=0,1,\dots}}
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
)
n
Pochhammer
𝑎
𝑛
{\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
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
