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Statements
F
(
a
,
b
1
2
(
a
+
b
+
1
)
;
z
)
=
(
1
-
z
-
1
-
1
1
-
z
-
1
+
1
)
a
F
(
a
,
1
2
(
a
+
b
)
a
+
b
;
4
1
-
z
-
1
(
1
-
z
-
1
+
1
)
2
)
,
Gauss-hypergeometric-F
𝑎
𝑏
1
2
𝑎
𝑏
1
𝑧
superscript
1
superscript
𝑧
1
1
1
superscript
𝑧
1
1
𝑎
Gauss-hypergeometric-F
𝑎
1
2
𝑎
𝑏
𝑎
𝑏
4
1
superscript
𝑧
1
superscript
1
superscript
𝑧
1
1
2
{\displaystyle{\displaystyle F\left({a,b\atop\tfrac{1}{2}(a+b+1)};z\right)=%
\left(\frac{\sqrt{1-z^{-1}}-1}{\sqrt{1-z^{-1}}+1}\right)^{a}F\left({a,\tfrac{1%
}{2}(a+b)\atop a+b};\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}}
b
𝑏
{\displaystyle{\displaystyle b}}
Identifiers
