Computation of a numerically satisfactory pair of solutions of the differential equation for conical functions of non-negative integer orders

Abstract

We consider the problem of computing satisfactory pairs of solutions of the differential equation for Legendre functions of non-negative integer order µ and degree −

Conical : An extended module for computing a numerically satisfactory pair of solutions of the differential equation for conical functions

“…The first order derivative of R m A preliminary algorithm for computing the function R m − 1 2 +iτ (x) was presented in [3] although the final algorithm in finite precision arithmetic implemented in the routine conicr presents some differences with respect to the first algorithm. We have also changed the notation of the function with respect to the one used in that reference; we are using now R m…”

“…For testing the expansions for R 0 − 1 2 +iτ (x) and R 1 − 1 2 +iτ (x) of section 2.1.1, we have used the Wronskian relation given in (3). In this case, we have…”