Computation of Legendre functions (Q1040305)

The authors develop methods for the computation of Legengre functions \(P_{\nu}(x)\), \(-1\leq x\leq 1\), \(\nu\in C\), the adjoint Legendre functions \(P_{\nu}^{-m}(x)\), \(m\in Z_{+}\), and their first derivatives. They used the Legendre differential equation and recurrence relations for \(P_{\nu}(x)\) and \(P_{\nu}'(x)\). They also based their results on integral representations given by \textit{E. T. Whittaker} and \textit{G. N. Watson} [A course of modern analysis. I. Translation from the English. 2nd ed. (Russian) (1963; Zbl 0108.26903)] and by \textit{I. M. Ryzhik} and \textit{I. S. Gradshtein} [Tafeln von Integralen, Summen, Reihen und Produkten. Moskau-Leningrad (1951; Zbl 0044.13303)].