Cohl (2011) gives a generalisation of the standard generating function for the Gegenbauer polynomials $ C_n^\mu(x)$ : $ (1 -2tx + t^2)^{-\nu} = A_{\mu,\nu} \frac{(1-t^2)^{-\nu+\mu+1/2}}{t^{\mu+1/2}} \sum_{n=0}^\infty (n+\mu) \: Q^{\nu-\mu-1/2}_{n+\mu-1/2}\left(\frac{1+t^2}{2t}\right) \: C^{\mu}_n(x)$ , where $ Q^\mu_\nu(x)$ are associated Legendre functions of the second kind, and $ A_{\mu,\nu} = \frac{\Gamma(\mu) e^{i\pi(\mu-\nu+1/2)}}{\sqrt{\pi}\Gamma(\nu)}$ . The traditional form is recoveredRead more