\[\mathsf{P}^{-\mu}_{\nu}\left(x\right)=\frac{1}{\left(\nu+\frac{1}{2}\right)^{1%
/4}2^{(\nu+\mu)/2}\Gamma\left(\frac{1}{2}\nu+\frac{1}{2}\mu+\frac{3}{4}\right)%
}\left(\frac{\zeta^{2}-\alpha^{2}}{x^{2}-a^{2}}\right)^{1/4}\*\left(U\left(\mu%
-\nu-\tfrac{1}{2},\left(2\nu+1\right)^{1/2}\zeta\right)+O\left(\nu^{-2/3}%
\right)\mathrm{env}\mskip-1.0muU\left(\mu-\nu-\tfrac{1}{2},\left(2\nu+1\right)%
^{1/2}\zeta\right)\right),\]