DLMF:15.8.E20
(Q5077)
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English
DLMF:15.8.E20
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Statements
Defining formula
F
(
a
,
1
-
a
c
;
z
)
=
(
1
-
z
)
c
-
1
F
(
1
2
(
c
-
a
)
,
1
2
(
a
+
c
-
1
)
c
;
4
z
(
1
-
z
)
)
,
Gauss-hypergeometric-F
𝑎
1
𝑎
𝑐
𝑧
superscript
1
𝑧
𝑐
1
Gauss-hypergeometric-F
1
2
𝑐
𝑎
1
2
𝑎
𝑐
1
𝑐
4
𝑧
1
𝑧
{\displaystyle{\displaystyle F\left({a,1-a\atop c};z\right)=(1-z)^{c-1}F\left(% {\frac{1}{2}(c-a),\frac{1}{2}(a+c-1)\atop c};4z(1-z)\right),}}
0 references
DLMF id
DLMF:15.8.E20
0 references
constraint
ℜ
z
<
1
2
𝑧
1
2
{\displaystyle{\displaystyle\Re z<\frac{1}{2}}}
0 references
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