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Statements
π
β‘
(
a
,
b
c
;
z
)
=
(
1
-
z
)
-
a
β’
π
β‘
(
a
,
c
-
b
c
;
z
z
-
1
)
=
(
1
-
z
)
-
b
β’
π
β‘
(
c
-
a
,
b
c
;
z
z
-
1
)
=
(
1
-
z
)
c
-
a
-
b
β’
π
β‘
(
c
-
a
,
c
-
b
c
;
z
)
,
scaled-hypergeometric-bold-F
π
π
π
π§
superscript
1
π§
π
scaled-hypergeometric-bold-F
π
π
π
π
π§
π§
1
superscript
1
π§
π
scaled-hypergeometric-bold-F
π
π
π
π
π§
π§
1
superscript
1
π§
π
π
π
scaled-hypergeometric-bold-F
π
π
π
π
π
π§
{\displaystyle{\displaystyle\mathbf{F}\left({a,b\atop c};z\right)=(1-z)^{-a}%
\mathbf{F}\left({a,c-b\atop c};\frac{z}{z-1}\right)=(1-z)^{-b}\mathbf{F}\left(%
{c-a,b\atop c};\frac{z}{z-1}\right)=(1-z)^{c-a-b}\mathbf{F}\left({c-a,c-b\atop
c%
};z\right),}}
|
ph
β‘
(
1
-
z
)
|
<
Ο
phase
1
π§
π
{\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}
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}}
c
π
{\displaystyle{\displaystyle c}}
Identifiers
