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Statements
w
5
(
z
)
=
e
a
π
i
z
-
a
F
(
a
,
a
-
c
+
1
a
-
b
+
1
;
1
z
)
=
e
(
c
-
b
)
π
i
z
b
-
c
(
1
-
z
)
c
-
a
-
b
F
(
1
-
b
,
c
-
b
a
-
b
+
1
;
1
z
)
=
(
1
-
z
)
-
a
F
(
a
,
c
-
b
a
-
b
+
1
;
1
1
-
z
)
=
e
(
c
-
1
)
π
i
z
1
-
c
(
1
-
z
)
c
-
a
-
1
F
(
1
-
b
,
a
-
c
+
1
a
-
b
+
1
;
1
1
-
z
)
.
subscript
𝑤
5
𝑧
superscript
𝑒
𝑎
𝜋
imaginary-unit
superscript
𝑧
𝑎
Gauss-hypergeometric-F
𝑎
𝑎
𝑐
1
𝑎
𝑏
1
1
𝑧
superscript
𝑒
𝑐
𝑏
𝜋
imaginary-unit
superscript
𝑧
𝑏
𝑐
superscript
1
𝑧
𝑐
𝑎
𝑏
Gauss-hypergeometric-F
1
𝑏
𝑐
𝑏
𝑎
𝑏
1
1
𝑧
superscript
1
𝑧
𝑎
Gauss-hypergeometric-F
𝑎
𝑐
𝑏
𝑎
𝑏
1
1
1
𝑧
superscript
𝑒
𝑐
1
𝜋
imaginary-unit
superscript
𝑧
1
𝑐
superscript
1
𝑧
𝑐
𝑎
1
Gauss-hypergeometric-F
1
𝑏
𝑎
𝑐
1
𝑎
𝑏
1
1
1
𝑧
{\displaystyle{\displaystyle w_{5}(z)=e^{a\pi\mathrm{i}}z^{-a}\*F\left({a,a-c+%
1\atop a-b+1};\frac{1}{z}\right)=e^{(c-b)\pi\mathrm{i}}z^{b-c}(1-z)^{c-a-b}\*F%
\left({1-b,c-b\atop a-b+1};\frac{1}{z}\right)=(1-z)^{-a}F\left({a,c-b\atop a-b%
+1};\frac{1}{1-z}\right)=e^{(c-1)\pi\mathrm{i}}z^{1-c}(1-z)^{c-a-1}\*F\left({1%
-b,a-c+1\atop a-b+1};\frac{1}{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)}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
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
