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Statements
w
2
(
z
)
=
z
1
-
c
F
(
a
-
c
+
1
,
b
-
c
+
1
2
-
c
;
z
)
=
z
1
-
c
(
1
-
z
)
c
-
a
-
b
F
(
1
-
a
,
1
-
b
2
-
c
;
z
)
=
z
1
-
c
(
1
-
z
)
c
-
a
-
1
F
(
a
-
c
+
1
,
1
-
b
2
-
c
;
z
z
-
1
)
=
z
1
-
c
(
1
-
z
)
c
-
b
-
1
F
(
1
-
a
,
b
-
c
+
1
2
-
c
;
z
z
-
1
)
.
subscript
𝑤
2
𝑧
superscript
𝑧
1
𝑐
Gauss-hypergeometric-F
𝑎
𝑐
1
𝑏
𝑐
1
2
𝑐
𝑧
superscript
𝑧
1
𝑐
superscript
1
𝑧
𝑐
𝑎
𝑏
Gauss-hypergeometric-F
1
𝑎
1
𝑏
2
𝑐
𝑧
superscript
𝑧
1
𝑐
superscript
1
𝑧
𝑐
𝑎
1
Gauss-hypergeometric-F
𝑎
𝑐
1
1
𝑏
2
𝑐
𝑧
𝑧
1
superscript
𝑧
1
𝑐
superscript
1
𝑧
𝑐
𝑏
1
Gauss-hypergeometric-F
1
𝑎
𝑏
𝑐
1
2
𝑐
𝑧
𝑧
1
{\displaystyle{\displaystyle w_{2}(z)={z^{1-c}}F\left({a-c+1,b-c+1\atop 2-c};z%
\right)={z^{1-c}(1-z)^{c-a-b}}\*F\left({1-a,1-b\atop 2-c};z\right)={z^{1-c}(1-%
z)^{c-a-1}}\*F\left({a-c+1,1-b\atop 2-c};\frac{z}{z-1}\right)={z^{1-c}(1-z)^{c%
-b-1}}\*F\left({1-a,b-c+1\atop 2-c};\frac{z}{z-1}\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)}}
z
𝑧
{\displaystyle{\displaystyle z}}
a
𝑎
{\displaystyle{\displaystyle a}}
b
𝑏
{\displaystyle{\displaystyle b}}
c
𝑐
{\displaystyle{\displaystyle c}}
w
m
(
z
)
subscript
𝑤
𝑚
𝑧
{\displaystyle{\displaystyle w_{m}(z)}}
Identifiers
