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Statements
F
q
+
1
p
(
a
1
,
…
,
a
p
b
0
,
…
,
b
q
;
z
)
=
Γ
(
b
0
)
2
π
i
∫
c
-
i
∞
c
+
i
∞
e
t
t
-
b
0
F
q
p
(
a
1
,
…
,
a
p
b
1
,
…
,
b
q
;
z
t
)
d
t
,
Gauss-hypergeometric-pFq
𝑝
𝑞
1
subscript
𝑎
1
…
subscript
𝑎
𝑝
subscript
𝑏
0
…
subscript
𝑏
𝑞
𝑧
Euler-Gamma
subscript
𝑏
0
2
𝜋
imaginary-unit
superscript
subscript
𝑐
imaginary-unit
𝑐
imaginary-unit
𝑡
superscript
𝑡
subscript
𝑏
0
Gauss-hypergeometric-pFq
𝑝
𝑞
subscript
𝑎
1
…
subscript
𝑎
𝑝
subscript
𝑏
1
…
subscript
𝑏
𝑞
𝑧
𝑡
𝑡
{\displaystyle{\displaystyle{{}_{p}F_{q+1}}\left({a_{1},\dots,a_{p}\atop b_{0}%
,\dots,b_{q}};z\right)=\frac{\Gamma\left(b_{0}\right)}{2\pi\mathrm{i}}\int_{c-%
\mathrm{i}\infty}^{c+\mathrm{i}\infty}{\mathrm{e}^{t}}t^{-b_{0}}{{}_{p}F_{q}}%
\left({a_{1},\dots,a_{p}\atop b_{1},\dots,b_{q}};\frac{z}{t}\right)\mathrm{d}t%
,}}
ℜ
b
0
>
0
subscript
𝑏
0
0
{\displaystyle{\displaystyle\Re b_{0}>0}}
c
>
0
𝑐
0
{\displaystyle{\displaystyle c>0}}
ℜ
b
0
>
0
subscript
𝑏
0
0
{\displaystyle{\displaystyle\Re b_{0}>0}}
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}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
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
