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Statements
w
2
(
z
)
=
e
(
1
-
a
)
π
i
Γ
(
2
-
c
)
Γ
(
c
-
b
)
Γ
(
a
-
c
+
1
)
Γ
(
c
-
a
-
b
+
1
)
w
4
(
z
)
+
e
-
a
π
i
Γ
(
2
-
c
)
Γ
(
c
-
b
)
Γ
(
a
-
b
+
1
)
Γ
(
1
-
a
)
w
5
(
z
)
,
subscript
𝑤
2
𝑧
superscript
𝑒
1
𝑎
𝜋
imaginary-unit
Euler-Gamma
2
𝑐
Euler-Gamma
𝑐
𝑏
Euler-Gamma
𝑎
𝑐
1
Euler-Gamma
𝑐
𝑎
𝑏
1
subscript
𝑤
4
𝑧
superscript
𝑒
𝑎
𝜋
imaginary-unit
Euler-Gamma
2
𝑐
Euler-Gamma
𝑐
𝑏
Euler-Gamma
𝑎
𝑏
1
Euler-Gamma
1
𝑎
subscript
𝑤
5
𝑧
{\displaystyle{\displaystyle w_{2}(z)=e^{(1-a)\pi\mathrm{i}}\frac{\Gamma\left(%
2-c\right)\Gamma\left(c-b\right)}{\Gamma\left(a-c+1\right)\Gamma\left(c-a-b+1%
\right)}w_{4}(z)+e^{-a\pi\mathrm{i}}\frac{\Gamma\left(2-c\right)\Gamma\left(c-%
b\right)}{\Gamma\left(a-b+1\right)\Gamma\left(1-a\right)}w_{5}(z),}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\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)}}
