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