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Statements
π
β‘
(
a
,
b
2
β’
b
;
z
)
=
Ο
Ξ
β‘
(
b
)
β’
z
-
b
+
(
1
/
2
)
β’
(
1
-
z
)
(
b
-
a
-
(
1
/
2
)
)
/
2
β’
P
a
-
b
-
(
1
/
2
)
-
b
+
(
1
/
2
)
β‘
(
2
-
z
2
β’
1
-
z
)
,
scaled-hypergeometric-bold-F
π
π
2
π
π§
π
Euler-Gamma
π
superscript
π§
π
1
2
superscript
1
π§
π
π
1
2
2
Legendre-P-first-kind
π
1
2
π
π
1
2
2
π§
2
1
π§
{\displaystyle{\displaystyle\mathbf{F}\left({a,b\atop 2b};z\right)=\frac{\sqrt%
{\pi}}{\Gamma\left(b\right)}z^{-b+(\ifrac{1}{2})}(1-z)^{(b-a-(\ifrac{1}{2}))/2%
}\*P^{-b+(\ifrac{1}{2})}_{a-b-(\ifrac{1}{2})}\left(\frac{2-z}{2\sqrt{1-z}}%
\right),}}
|
ph
β‘
(
1
-
z
)
|
<
Ο
phase
1
π§
π
{\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}
|
ph
β‘
(
1
-
z
)
|
<
Ο
ph
1
π§
π
{\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}
|
1
-
z
|
<
1
1
π§
1
{\displaystyle{\displaystyle|1-z|<1}}
Ξ
β‘
(
z
)
Euler-Gamma
π§
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
P
Ξ½
ΞΌ
β‘
(
z
)
Legendre-P-first-kind
π
π
π§
{\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
Ο
{\displaystyle{\displaystyle\pi}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
π
β‘
(
a
,
b
;
c
;
z
)
scaled-hypergeometric-bold-F
π
π
π
π§
{\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z%
}\right)}}
z
π§
{\displaystyle{\displaystyle z}}
a
π
{\displaystyle{\displaystyle a}}
b
π
{\displaystyle{\displaystyle b}}
Identifiers
