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