\[F\left(3a,a;2a;{\mathrm{e}}^{\ifrac{\mathrm{i}\pi}{3}}\right)=\sqrt{\pi}{%
\mathrm{e}}^{\ifrac{\mathrm{i}\pi a}{2}}\frac{2^{2a}\Gamma\left(\frac{1}{2}+a%
\right)}{3^{(3a+1)/2}}\left(\frac{1}{\Gamma\left(\frac{1}{3}+a\right)\Gamma%
\left(\frac{2}{3}\right)}+\frac{1}{\Gamma\left(\frac{2}{3}+a\right)\Gamma\left%
(\frac{1}{3}\right)}\right),\]