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Statements
F
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Γ
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1
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.
Gauss-hypergeometric-pFq
𝑝
𝑞
subscript
𝑎
1
…
subscript
𝑎
𝑝
subscript
𝑏
1
…
subscript
𝑏
𝑞
𝑧
superscript
subscript
product
𝑘
1
𝑞
Euler-Gamma
subscript
𝑏
𝑘
superscript
subscript
product
𝑘
1
𝑝
Euler-Gamma
subscript
𝑎
𝑘
Meijer-G
1
𝑝
𝑝
𝑞
1
𝑧
1
subscript
𝑎
1
…
1
subscript
𝑎
𝑝
0
1
subscript
𝑏
1
…
1
subscript
𝑏
𝑞
superscript
subscript
product
𝑘
1
𝑞
Euler-Gamma
subscript
𝑏
𝑘
superscript
subscript
product
𝑘
1
𝑝
Euler-Gamma
subscript
𝑎
𝑘
Meijer-G
𝑝
1
𝑞
1
𝑝
1
𝑧
1
subscript
𝑏
1
…
subscript
𝑏
𝑞
subscript
𝑎
1
…
subscript
𝑎
𝑝
{\displaystyle{\displaystyle{{}_{p}F_{q}}\left({a_{1},\dots,a_{p}\atop b_{1},%
\dots,b_{q}};z\right)=\left({\textstyle\ifrac{\prod\limits_{k=1}^{q}\Gamma%
\left(b_{k}\right)}{\prod\limits_{k=1}^{p}\Gamma\left(a_{k}\right)}}\right){G^%
{1,p}_{p,q+1}}\left(-z;{1-a_{1},\dots,1-a_{p}\atop 0,1-b_{1},\dots,1-b_{q}}%
\right)=\left({\textstyle\ifrac{\prod\limits_{k=1}^{q}\Gamma\left(b_{k}\right)%
}{\prod\limits_{k=1}^{p}\Gamma\left(a_{k}\right)}}\right){G^{p,1}_{q+1,p}}%
\left(-\frac{1}{z};{1,b_{1},\dots,b_{q}\atop a_{1},\dots,a_{p}}\right).}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
F
q
p
(
a
1
,
…
,
a
p
;
b
1
,
…
,
b
q
;
z
)
Gauss-hypergeometric-pFq
𝑝
𝑞
subscript
𝑎
1
…
subscript
𝑎
𝑝
subscript
𝑏
1
…
subscript
𝑏
𝑞
𝑧
{\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots%
,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}
G
p
,
q
m
,
n
(
z
;
a
1
,
…
,
a
p
b
1
,
…
,
b
q
)
Meijer-G
𝑚
𝑛
𝑝
𝑞
𝑧
subscript
𝑎
1
…
subscript
𝑎
𝑝
subscript
𝑏
1
…
subscript
𝑏
𝑞
{\displaystyle{\displaystyle{G^{\NVar{m},\NVar{n}}_{\NVar{p},\NVar{q}}}\left(%
\NVar{z};{\NVar{a_{1},\dots,a_{p}}\atop\NVar{b_{1},\dots,b_{q}}}\right)}}
p
𝑝
{\displaystyle{\displaystyle p}}
q
𝑞
{\displaystyle{\displaystyle q}}
z
𝑧
{\displaystyle{\displaystyle z}}
a
,
a
1
,
…
,
a
p
𝑎
subscript
𝑎
1
…
subscript
𝑎
𝑝
{\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}
b
,
b
1
,
…
,
b
q
𝑏
subscript
𝑏
1
…
subscript
𝑏
𝑞
{\displaystyle{\displaystyle b,b_{1},\ldots,b_{q}}}
Identifiers
