Large-parameter asymptotic expansions for the Legendre and allied functions

Gergő Nemes, Adri B. Olde Daalhuis

Surprisingly, apart from some special cases, simple asymptotic expansions for the associated Legendre functions $P_{\nu }^{\mu }(z)$ and $Q_{\nu }^{\mu }(z)$ for large degree $\nu$ or large order $\mu$ ar…