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DLMF:15.1.E2 - MaRDI portal
Statements
F
β‘
(
a
,
b
;
c
;
z
)
Ξ
β‘
(
c
)
=
π
β‘
(
a
,
b
;
c
;
z
)
=
π
β‘
(
a
,
b
c
;
z
)
=
π
1
2
β‘
(
a
,
b
;
c
;
z
)
,
Gauss-hypergeometric-F
π
π
π
π§
Euler-Gamma
π
scaled-hypergeometric-bold-F
π
π
π
π§
scaled-hypergeometric-bold-F
π
π
π
π§
hypergeometric-bold-pFq
2
1
π
π
π
π§
{\displaystyle{\displaystyle\frac{F\left(a,b;c;z\right)}{\Gamma\left(c\right)}%
=\mathbf{F}\left(a,b;c;z\right)=\mathbf{F}\left({a,b\atop c};z\right)={{}_{2}{%
\mathbf{F}}_{1}}\left(a,b;c;z\right),}}
Ξ
β‘
(
z
)
Euler-Gamma
π§
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
F
β‘
(
a
,
b
;
c
;
z
)
Gauss-hypergeometric-F
π
π
π
π§
{\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}
π
q
p
β‘
(
π
;
π
;
)
hypergeometric-bold-pFq
π
π
π
π
{\displaystyle{\displaystyle{{}_{\NVar{p}}{\mathbf{F}}_{\NVar{q}}}\left(\NVar{%
\mathbf{a}};\NVar{\mathbf{b}};\right)\)\@add@PDF@RDFa@triples\end{document}}}
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