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Statements
F
q
q
+
1
(
a
1
,
…
,
a
q
+
1
b
1
,
…
,
b
q
;
z
)
=
∑
j
=
1
q
+
1
(
∏
k
=
1
k
≠
j
q
+
1
Γ
(
a
k
-
a
j
)
Γ
(
a
k
)
/
∏
k
=
1
q
Γ
(
b
k
-
a
j
)
Γ
(
b
k
)
)
w
~
j
(
z
)
,
Gauss-hypergeometric-pFq
𝑞
1
𝑞
subscript
𝑎
1
…
subscript
𝑎
𝑞
1
subscript
𝑏
1
…
subscript
𝑏
𝑞
𝑧
superscript
subscript
𝑗
1
𝑞
1
superscript
subscript
product
𝑘
1
𝑘
𝑗
𝑞
1
Euler-Gamma
subscript
𝑎
𝑘
subscript
𝑎
𝑗
Euler-Gamma
subscript
𝑎
𝑘
superscript
subscript
product
𝑘
1
𝑞
Euler-Gamma
subscript
𝑏
𝑘
subscript
𝑎
𝑗
Euler-Gamma
subscript
𝑏
𝑘
subscript
~
𝑤
𝑗
𝑧
{\displaystyle{\displaystyle{{}_{q+1}F_{q}}\left({a_{1},\dots,a_{q+1}\atop b_{%
1},\dots,b_{q}};z\right)=\sum_{j=1}^{q+1}\left({\textstyle\ifrac{\prod\limits_%
{\begin{subarray}{c}k=1\\
k\neq j\end{subarray}}^{q+1}\frac{\Gamma\left(a_{k}-a_{j}\right)}{\Gamma\left(%
a_{k}\right)}}{\prod\limits_{k=1}^{q}\frac{\Gamma\left(b_{k}-a_{j}\right)}{%
\Gamma\left(b_{k}\right)}}}\right)\widetilde{w}_{j}(z),}}
|
ph
(
-
z
)
|
≤
π
phase
𝑧
𝜋
{\displaystyle{\displaystyle|\operatorname{ph}\left(-z\right)|\leq\pi}}
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)}}
π
{\displaystyle{\displaystyle\pi}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
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}}}
w
𝑤
{\displaystyle{\displaystyle w}}
Identifiers
