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