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Statements
z
(
1
-
z
)
(
d
F
(
a
,
b
;
c
;
z
)
/
d
z
)
=
(
c
-
a
)
F
(
a
-
1
,
b
;
c
;
z
)
+
(
a
-
c
+
b
z
)
F
(
a
,
b
;
c
;
z
)
=
(
c
-
b
)
F
(
a
,
b
-
1
;
c
;
z
)
+
(
b
-
c
+
a
z
)
F
(
a
,
b
;
c
;
z
)
,
𝑧
1
𝑧
derivative
Gauss-hypergeometric-F
𝑎
𝑏
𝑐
𝑧
𝑧
𝑐
𝑎
Gauss-hypergeometric-F
𝑎
1
𝑏
𝑐
𝑧
𝑎
𝑐
𝑏
𝑧
Gauss-hypergeometric-F
𝑎
𝑏
𝑐
𝑧
𝑐
𝑏
Gauss-hypergeometric-F
𝑎
𝑏
1
𝑐
𝑧
𝑏
𝑐
𝑎
𝑧
Gauss-hypergeometric-F
𝑎
𝑏
𝑐
𝑧
{\displaystyle{\displaystyle z(1-z)\left(\ifrac{\mathrm{d}F\left(a,b;c;z\right%
)}{\mathrm{d}z}\right)=(c-a)F\left(a-1,b;c;z\right)+(a-c+bz)F\left(a,b;c;z%
\right)=(c-b)F\left(a,b-1;c;z\right)+(b-c+az)F\left(a,b;c;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)}}
d
f
d
x
derivative
𝑓
𝑥
{\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
z
𝑧
{\displaystyle{\displaystyle z}}
a
𝑎
{\displaystyle{\displaystyle a}}
b
𝑏
{\displaystyle{\displaystyle b}}
c
𝑐
{\displaystyle{\displaystyle c}}
Identifiers
