\[\mathsf{P}^{\mu}_{\nu}\left(x\right)=\frac{2^{\mu}\Gamma\left(1-2\mu\right)%
\Gamma\left(\nu+\mu+1\right)}{\Gamma\left(\nu-\mu+1\right)\Gamma\left(1-\mu%
\right)\left(1-x^{2}\right)^{\mu/2}}C^{(\frac{1}{2}-\mu)}_{\nu+\mu}\left(x%
\right).\]