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