\[\mathsf{P}^{-\mu}_{\nu}\left(\pm x\right)=\left(\frac{1\mp x}{1\pm x}\right)^{%
\mu/2}\left(\sum_{j=0}^{J-1}\frac{{\left(\nu+1\right)_{j}}{\left(-\nu\right)_{%
j}}}{j!\Gamma\left(j+1+\mu\right)}\left(\frac{1\mp x}{2}\right)^{j}+O\left(%
\frac{1}{\Gamma\left(J+1+\mu\right)}\right)\right)\]