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Statements
w
4
(
z
)
=
(
1
-
z
)
c
-
a
-
b
F
(
c
-
a
,
c
-
b
c
-
a
-
b
+
1
;
1
-
z
)
=
z
1
-
c
(
1
-
z
)
c
-
a
-
b
F
(
1
-
a
,
1
-
b
c
-
a
-
b
+
1
;
1
-
z
)
=
z
a
-
c
(
1
-
z
)
c
-
a
-
b
F
(
1
-
a
,
c
-
a
c
-
a
-
b
+
1
;
1
-
1
z
)
=
z
b
-
c
(
1
-
z
)
c
-
a
-
b
F
(
1
-
b
,
c
-
b
c
-
a
-
b
+
1
;
1
-
1
z
)
.
subscript
𝑤
4
𝑧
superscript
1
𝑧
𝑐
𝑎
𝑏
Gauss-hypergeometric-F
𝑐
𝑎
𝑐
𝑏
𝑐
𝑎
𝑏
1
1
𝑧
superscript
𝑧
1
𝑐
superscript
1
𝑧
𝑐
𝑎
𝑏
Gauss-hypergeometric-F
1
𝑎
1
𝑏
𝑐
𝑎
𝑏
1
1
𝑧
superscript
𝑧
𝑎
𝑐
superscript
1
𝑧
𝑐
𝑎
𝑏
Gauss-hypergeometric-F
1
𝑎
𝑐
𝑎
𝑐
𝑎
𝑏
1
1
1
𝑧
superscript
𝑧
𝑏
𝑐
superscript
1
𝑧
𝑐
𝑎
𝑏
Gauss-hypergeometric-F
1
𝑏
𝑐
𝑏
𝑐
𝑎
𝑏
1
1
1
𝑧
{\displaystyle{\displaystyle w_{4}(z)=(1-z)^{c-a-b}F\left({c-a,c-b\atop c-a-b+%
1};1-z\right)=z^{1-c}(1-z)^{c-a-b}F\left({1-a,1-b\atop c-a-b+1};1-z\right)=z^{%
a-c}(1-z)^{c-a-b}F\left({1-a,c-a\atop c-a-b+1};1-\frac{1}{z}\right)=z^{b-c}(1-%
z)^{c-a-b}F\left({1-b,c-b\atop c-a-b+1};1-\frac{1}{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)}}
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
