\[P_{j}^{5}=\frac{{\left(\alpha\right)_{j}}{\left(1-\gamma+\alpha\right)_{j}}}{{%
\left(1+\alpha-\beta+\epsilon\right)_{2j}}}z^{-\alpha-j}\*{{}_{2}F_{1}}\left({%
\alpha+j,1-\gamma+\alpha+j\atop 1+\alpha-\beta+\epsilon+2j};\frac{1}{z}\right),\]