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Statements
(
z
d
d
z
z
)
n
(
z
γ
-
1
F
q
p
+
1
(
γ
,
a
1
,
…
,
a
p
b
1
,
…
,
b
q
;
z
)
)
=
(
γ
)
n
z
γ
+
n
-
1
F
q
p
+
1
(
γ
+
n
,
a
1
,
…
,
a
p
b
1
,
…
,
b
q
;
z
)
,
superscript
𝑧
derivative
𝑧
𝑧
𝑛
superscript
𝑧
𝛾
1
Gauss-hypergeometric-pFq
𝑝
1
𝑞
𝛾
subscript
𝑎
1
…
subscript
𝑎
𝑝
subscript
𝑏
1
…
subscript
𝑏
𝑞
𝑧
Pochhammer
𝛾
𝑛
superscript
𝑧
𝛾
𝑛
1
Gauss-hypergeometric-pFq
𝑝
1
𝑞
𝛾
𝑛
subscript
𝑎
1
…
subscript
𝑎
𝑝
subscript
𝑏
1
…
subscript
𝑏
𝑞
𝑧
{\displaystyle{\displaystyle\left(z\frac{\mathrm{d}}{\mathrm{d}z}z\right)^{n}%
\left(z^{\gamma-1}{{}_{p+1}F_{q}}\left({\gamma,a_{1},\dots,a_{p}\atop b_{1},%
\dots,b_{q}};z\right)\right)={\left(\gamma\right)_{n}}z^{\gamma+n-1}{{}_{p+1}F%
_{q}}\left({\gamma+n,a_{1},\dots,a_{p}\atop b_{1},\dots,b_{q}};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)}}
(
a
)
n
Pochhammer
𝑎
𝑛
{\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
d
f
d
x
derivative
𝑓
𝑥
{\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
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
