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Statements
sin
(
π
(
c
-
a
-
b
)
)
π
𝐅
(
a
,
b
c
;
z
)
=
z
-
a
Γ
(
c
-
a
)
Γ
(
c
-
b
)
𝐅
(
a
,
a
-
c
+
1
a
+
b
-
c
+
1
;
1
-
1
z
)
-
(
1
-
z
)
c
-
a
-
b
z
a
-
c
Γ
(
a
)
Γ
(
b
)
𝐅
(
c
-
a
,
1
-
a
c
-
a
-
b
+
1
;
1
-
1
z
)
,
𝜋
𝑐
𝑎
𝑏
𝜋
scaled-hypergeometric-bold-F
𝑎
𝑏
𝑐
𝑧
superscript
𝑧
𝑎
Euler-Gamma
𝑐
𝑎
Euler-Gamma
𝑐
𝑏
scaled-hypergeometric-bold-F
𝑎
𝑎
𝑐
1
𝑎
𝑏
𝑐
1
1
1
𝑧
superscript
1
𝑧
𝑐
𝑎
𝑏
superscript
𝑧
𝑎
𝑐
Euler-Gamma
𝑎
Euler-Gamma
𝑏
scaled-hypergeometric-bold-F
𝑐
𝑎
1
𝑎
𝑐
𝑎
𝑏
1
1
1
𝑧
{\displaystyle{\displaystyle\frac{\sin\left(\pi(c-a-b)\right)}{\pi}\mathbf{F}%
\left({a,b\atop c};z\right)=\frac{z^{-a}}{\Gamma\left(c-a\right)\Gamma\left(c-%
b\right)}\mathbf{F}\left({a,a-c+1\atop a+b-c+1};1-\frac{1}{z}\right)-\frac{(1-%
z)^{c-a-b}z^{a-c}}{\Gamma\left(a\right)\Gamma\left(b\right)}\mathbf{F}\left({c%
-a,1-a\atop c-a-b+1};1-\frac{1}{z}\right),}}
|
ph
z
|
<
π
phase
𝑧
𝜋
{\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}
|
ph
(
1
-
z
)
|
<
π
phase
1
𝑧
𝜋
{\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
𝐅
(
a
,
b
;
c
;
z
)
scaled-hypergeometric-bold-F
𝑎
𝑏
𝑐
𝑧
{\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z%
}\right)}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
z
𝑧
{\displaystyle{\displaystyle z}}
a
𝑎
{\displaystyle{\displaystyle a}}
b
𝑏
{\displaystyle{\displaystyle b}}
c
𝑐
{\displaystyle{\displaystyle c}}
Identifiers
