\[P^{\mu}_{\nu}\left(x\right)=(2/\pi)^{1/2}\left(x^{2}-1\right)^{-1/4}\*%
\boldsymbol{Q}^{\nu+(1/2)}_{-\mu-(1/2)}\left(x\left(x^{2}-1\right)^{-1/2}%
\right).\]