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Statements
F
2
3
(
a
,
2
b
-
a
-
1
,
2
-
2
b
+
a
b
,
a
-
b
+
3
2
;
z
4
)
=
(
1
-
z
)
-
a
F
2
3
(
1
3
a
,
1
3
a
+
1
3
,
1
3
a
+
2
3
b
,
a
-
b
+
3
2
;
-
27
z
4
(
1
-
z
)
3
)
.
Gauss-hypergeometric-pFq
3
2
𝑎
2
𝑏
𝑎
1
2
2
𝑏
𝑎
𝑏
𝑎
𝑏
3
2
𝑧
4
superscript
1
𝑧
𝑎
Gauss-hypergeometric-pFq
3
2
1
3
𝑎
1
3
𝑎
1
3
1
3
𝑎
2
3
𝑏
𝑎
𝑏
3
2
27
𝑧
4
superscript
1
𝑧
3
{\displaystyle{\displaystyle{{}_{3}F_{2}}\left({a,2b-a-1,2-2b+a\atop b,a-b+%
\frac{3}{2}};\frac{z}{4}\right)=(1-z)^{-a}{{}_{3}F_{2}}\left({\frac{1}{3}a,%
\frac{1}{3}a+\frac{1}{3},\frac{1}{3}a+\frac{2}{3}\atop b,a-b+\frac{3}{2}};%
\frac{-27z}{4(1-z)^{3}}\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)}}
z
𝑧
{\displaystyle{\displaystyle z}}
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
