\[\mathsf{P}^{-\mu}_{\nu}\left(\cos\theta\right)=\frac{1}{\nu^{\mu}}\left(\frac{%
\theta}{\sin\theta}\right)^{1/2}\left(J_{\mu}\left(\left(\nu+\tfrac{1}{2}%
\right)\theta\right)+O\left(\frac{1}{\nu}\right)\operatorname{env}\mskip-2.0%
muJ_{\mu}\left(\left(\nu+\tfrac{1}{2}\right)\theta\right)\right),\]