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Statements
F
(
a
,
1
-
a
c
;
z
)
=
(
1
-
z
-
1
-
1
)
1
-
a
(
1
-
z
-
1
+
1
)
a
-
2
c
+
1
(
1
-
z
-
1
)
c
-
1
F
(
c
-
a
,
c
-
1
2
2
c
-
1
;
4
1
-
z
-
1
(
1
-
z
-
1
+
1
)
2
)
,
Gauss-hypergeometric-F
𝑎
1
𝑎
𝑐
𝑧
superscript
1
superscript
𝑧
1
1
1
𝑎
superscript
1
superscript
𝑧
1
1
𝑎
2
𝑐
1
superscript
1
superscript
𝑧
1
𝑐
1
Gauss-hypergeometric-F
𝑐
𝑎
𝑐
1
2
2
𝑐
1
4
1
superscript
𝑧
1
superscript
1
superscript
𝑧
1
1
2
{\displaystyle{\displaystyle F\left({a,1-a\atop c};z\right)=\left(\sqrt{1-z^{-%
1}}-1\right)^{1-a}\left(\sqrt{1-z^{-1}}+1\right)^{a-2c+1}\left(1-z^{-1}\right)%
^{c-1}F\left({c-a,c-\tfrac{1}{2}\atop 2c-1};\frac{4\sqrt{1-z^{-1}}}{\left(%
\sqrt{1-z^{-1}}+1\right)^{2}}\right),}}
|
ph
(
-
z
)
|
<
π
phase
𝑧
𝜋
{\displaystyle{\displaystyle|\operatorname{ph}\left(-z\right)|<\pi}}
ℜ
z
<
1
2
𝑧
1
2
{\displaystyle{\displaystyle\Re z<\frac{1}{2}}}
F
(
a
,
b
;
c
;
z
)
Gauss-hypergeometric-F
𝑎
𝑏
𝑐
𝑧
{\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
z
𝑧
{\displaystyle{\displaystyle z}}
a
𝑎
{\displaystyle{\displaystyle a}}
c
𝑐
{\displaystyle{\displaystyle c}}
Identifiers
