DLMF:15.8.E32 (Q5089)

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Language	Label	Description	Also known as
English	DLMF:15.8.E32	No description defined

Statements

{\displaystyle{\displaystyle\frac{\left(1-z^{3}\right)^{a}}{\left(-z\right)^{3% a}}\left(\frac{1}{\Gamma\left(a+\frac{2}{3}\right)\Gamma\left(\frac{2}{3}% \right)}F\left({a,a+\frac{1}{3}\atop\frac{2}{3}};z^{-3}\right)+\frac{e^{\frac{% 1}{3}\pi\mathrm{i}}}{z\Gamma\left(a\right)\Gamma\left(\frac{4}{3}\right)}F% \left({a+\frac{1}{3},a+\frac{2}{3}\atop\frac{4}{3}};z^{-3}\right)\right)=\frac% {3^{\frac{3}{2}a+\frac{1}{2}}e^{\frac{1}{2}a\pi\mathrm{i}}\Gamma\left(a+\frac{% 1}{3}\right)(1-\zeta)^{a}}{2\pi\Gamma\left(2a+\frac{2}{3}\right)(-\zeta)^{2a}}% F\left({a+\frac{1}{3},3a\atop 2a+\frac{2}{3}};\zeta^{-1}\right),}}

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DLMF:15.8.E32

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{\displaystyle{\displaystyle|\operatorname{ph}\left(-z\right)|<\frac{1}{3}\pi}}

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