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Statements
(
(
1
-
z
)
d
d
z
(
1
-
z
)
)
n
(
(
1
-
z
)
a
-
1
F
(
a
,
b
;
c
;
z
)
)
=
(
-
1
)
n
(
a
)
n
(
c
-
b
)
n
(
c
)
n
(
1
-
z
)
a
+
n
-
1
F
(
a
+
n
,
b
;
c
+
n
;
z
)
.
superscript
1
𝑧
derivative
𝑧
1
𝑧
𝑛
superscript
1
𝑧
𝑎
1
Gauss-hypergeometric-F
𝑎
𝑏
𝑐
𝑧
superscript
1
𝑛
Pochhammer
𝑎
𝑛
Pochhammer
𝑐
𝑏
𝑛
Pochhammer
𝑐
𝑛
superscript
1
𝑧
𝑎
𝑛
1
Gauss-hypergeometric-F
𝑎
𝑛
𝑏
𝑐
𝑛
𝑧
{\displaystyle{\displaystyle\left((1-z)\frac{\mathrm{d}}{\mathrm{d}z}(1-z)%
\right)^{n}\left((1-z)^{a-1}F\left(a,b;c;z\right)\right)=(-1)^{n}\frac{{\left(%
a\right)_{n}}{\left(c-b\right)_{n}}}{{\left(c\right)_{n}}}(1-z)^{a+n-1}\*F%
\left(a+n,b;c+n;z\right).}}
F
(
a
,
b
;
c
;
z
)
Gauss-hypergeometric-F
𝑎
𝑏
𝑐
𝑧
{\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\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}}}}
n
𝑛
{\displaystyle{\displaystyle n}}
z
𝑧
{\displaystyle{\displaystyle z}}
a
𝑎
{\displaystyle{\displaystyle a}}
b
𝑏
{\displaystyle{\displaystyle b}}
c
𝑐
{\displaystyle{\displaystyle c}}
Identifiers
