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