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Statements
2
z
Γ
(
-
1
2
)
Γ
(
a
+
b
-
1
2
)
Γ
(
a
-
1
2
)
Γ
(
b
-
1
2
)
F
(
a
,
b
;
3
2
;
z
)
=
F
(
2
a
-
1
,
2
b
-
1
;
a
+
b
-
1
2
;
1
2
-
1
2
z
)
-
F
(
2
a
-
1
,
2
b
-
1
;
a
+
b
-
1
2
;
1
2
+
1
2
z
)
,
2
𝑧
Euler-Gamma
1
2
Euler-Gamma
𝑎
𝑏
1
2
Euler-Gamma
𝑎
1
2
Euler-Gamma
𝑏
1
2
Gauss-hypergeometric-F
𝑎
𝑏
3
2
𝑧
Gauss-hypergeometric-F
2
𝑎
1
2
𝑏
1
𝑎
𝑏
1
2
1
2
1
2
𝑧
Gauss-hypergeometric-F
2
𝑎
1
2
𝑏
1
𝑎
𝑏
1
2
1
2
1
2
𝑧
{\displaystyle{\displaystyle\frac{2\sqrt{z}\Gamma\left(-\tfrac{1}{2}\right)%
\Gamma\left(a+b-\tfrac{1}{2}\right)}{\Gamma\left(a-\tfrac{1}{2}\right)\Gamma%
\left(b-\tfrac{1}{2}\right)}F\left(a,b;\tfrac{3}{2};z\right)=F\left(2a-1,2b-1;%
a+b-\tfrac{1}{2};\tfrac{1}{2}-\tfrac{1}{2}\sqrt{z}\right)-F\left(2a-1,2b-1;a+b%
-\tfrac{1}{2};\tfrac{1}{2}+\tfrac{1}{2}\sqrt{z}\right),}}
|
ph
z
|
<
π
phase
𝑧
𝜋
{\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}
|
ph
(
1
-
z
)
|
<
π
phase
1
𝑧
𝜋
{\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
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}}}
z
𝑧
{\displaystyle{\displaystyle z}}
a
𝑎
{\displaystyle{\displaystyle a}}
b
𝑏
{\displaystyle{\displaystyle b}}
Identifiers
