# DLMF:15.8.E3 (Q5060)

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DLMF:15.8.E3
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## Statements

${\displaystyle{\displaystyle\frac{\sin\left(\pi(b-a)\right)}{\pi}\mathbf{F}% \left({a,b\atop c};z\right)=\frac{(1-z)^{-a}}{\Gamma\left(b\right)\Gamma\left(% c-a\right)}\mathbf{F}\left({a,c-b\atop a-b+1};\frac{1}{1-z}\right)-\frac{(1-z)% ^{-b}}{\Gamma\left(a\right)\Gamma\left(c-b\right)}\mathbf{F}\left({b,c-a\atop b% -a+1};\frac{1}{1-z}\right),}}$
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DLMF:15.8.E3
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${\displaystyle{\displaystyle|\operatorname{ph}\left(-z\right)|<\pi}}$
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${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$
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${\displaystyle{\displaystyle\pi}}$
C3.S12.E1.m2abdec
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${\displaystyle{\displaystyle\operatorname{ph}}}$
C1.S9.E7.m1abdec
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${\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z% }\right)}}$
C15.S2.E2.m2abdec
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${\displaystyle{\displaystyle\sin\NVar{z}}}$
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${\displaystyle{\displaystyle z}}$
C15.S1.XMD3.m1bdec
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${\displaystyle{\displaystyle a}}$
C15.S1.XMD4.m1bdec
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${\displaystyle{\displaystyle b}}$
C15.S1.XMD5.m1bdec
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${\displaystyle{\displaystyle c}}$
C15.S1.XMD6.m1bdec
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