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Statements
π
β‘
(
a
,
b
c
;
x
+
i
β’
0
)
-
π
β‘
(
a
,
b
c
;
x
-
i
β’
0
)
=
2
β’
Ο
β’
i
Ξ
β‘
(
a
)
β’
Ξ
β‘
(
b
)
β’
(
x
-
1
)
c
-
a
-
b
β’
π
β‘
(
c
-
a
,
c
-
b
c
-
a
-
b
+
1
;
1
-
x
)
,
scaled-hypergeometric-bold-F
π
π
π
π₯
imaginary-unit
0
scaled-hypergeometric-bold-F
π
π
π
π₯
imaginary-unit
0
2
π
imaginary-unit
Euler-Gamma
π
Euler-Gamma
π
superscript
π₯
1
π
π
π
scaled-hypergeometric-bold-F
π
π
π
π
π
π
π
1
1
π₯
{\displaystyle{\displaystyle\mathbf{F}\left({a,b\atop c};x+\mathrm{i}0\right)-%
\mathbf{F}\left({a,b\atop c};x-\mathrm{i}0\right)=\frac{2\pi\mathrm{i}}{\Gamma%
\left(a\right)\Gamma\left(b\right)}(x-1)^{c-a-b}\mathbf{F}\left({c-a,c-b\atop c%
-a-b+1};1-x\right),}}
x
>
1
π₯
1
{\displaystyle{\displaystyle x>1}}
Ξ
β‘
(
z
)
Euler-Gamma
π§
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
Ο
{\displaystyle{\displaystyle\pi}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
π
β‘
(
a
,
b
;
c
;
z
)
scaled-hypergeometric-bold-F
π
π
π
π§
{\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z%
}\right)}}
x
π₯
{\displaystyle{\displaystyle x}}
a
π
{\displaystyle{\displaystyle a}}
b
π
{\displaystyle{\displaystyle b}}
c
π
{\displaystyle{\displaystyle c}}
Identifiers
