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Statements
F
6
7
(
a
,
1
2
a
+
1
,
b
,
c
,
d
,
e
,
f
1
2
a
,
a
-
b
+
1
,
a
-
c
+
1
,
a
-
d
+
1
,
a
-
e
+
1
,
a
-
f
+
1
;
1
)
=
Γ
(
a
-
d
+
1
)
Γ
(
a
-
e
+
1
)
Γ
(
a
-
f
+
1
)
Γ
(
a
-
d
-
e
-
f
+
1
)
Γ
(
a
+
1
)
Γ
(
a
-
d
-
e
+
1
)
Γ
(
a
-
d
-
f
+
1
)
Γ
(
a
-
e
-
f
+
1
)
F
3
4
(
a
-
b
-
c
+
1
,
d
,
e
,
f
a
-
b
+
1
,
a
-
c
+
1
,
d
+
e
+
f
-
a
;
1
)
,
Gauss-hypergeometric-pFq
7
6
𝑎
1
2
𝑎
1
𝑏
𝑐
𝑑
𝑒
𝑓
1
2
𝑎
𝑎
𝑏
1
𝑎
𝑐
1
𝑎
𝑑
1
𝑎
𝑒
1
𝑎
𝑓
1
1
Euler-Gamma
𝑎
𝑑
1
Euler-Gamma
𝑎
𝑒
1
Euler-Gamma
𝑎
𝑓
1
Euler-Gamma
𝑎
𝑑
𝑒
𝑓
1
Euler-Gamma
𝑎
1
Euler-Gamma
𝑎
𝑑
𝑒
1
Euler-Gamma
𝑎
𝑑
𝑓
1
Euler-Gamma
𝑎
𝑒
𝑓
1
Gauss-hypergeometric-pFq
4
3
𝑎
𝑏
𝑐
1
𝑑
𝑒
𝑓
𝑎
𝑏
1
𝑎
𝑐
1
𝑑
𝑒
𝑓
𝑎
1
{\displaystyle{\displaystyle{{}_{7}F_{6}}\left({a,\frac{1}{2}a+1,b,c,d,e,f%
\atop\frac{1}{2}a,a-b+1,a-c+1,a-d+1,a-e+1,a-f+1};1\right)=\frac{\Gamma\left(a-%
d+1\right)\Gamma\left(a-e+1\right)\Gamma\left(a-f+1\right)\Gamma\left(a-d-e-f+%
1\right)}{\Gamma\left(a+1\right)\Gamma\left(a-d-e+1\right)\Gamma\left(a-d-f+1%
\right)\Gamma\left(a-e-f+1\right)}{{}_{4}F_{3}}\left({a-b-c+1,d,e,f\atop a-b+1%
,a-c+1,d+e+f-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)}}
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
