\[P^{-\mu}_{\nu}\left(x\right)=\left(\frac{2\mu}{\pi}\right)^{1/2}\frac{1}{%
\Gamma\left(\mu+1\right)}\left(\frac{1-\alpha}{1+\alpha}\right)^{(\nu/2)+(1/4)%
}\*\left(1-\alpha^{2}\right)^{-\mu/2}\left(\frac{\alpha^{2}+\eta^{2}}{\alpha^{%
2}\left(x^{2}-1\right)+1}\right)^{1/4}\*K_{\nu+\frac{1}{2}}\left(\mu\eta\right%
)\left(1+O\left(\frac{1}{\mu}\right)\right),\]