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

摘要

Conical functions appear in a large number of applications in physics andengineering. In this paper we describe an extension of our module CONICAL forthe computation of conical functions. Specifically, the module includes now aroutine for computing the function ${{\rm R}}^{m}_{-\frac{1}{2}+i\tau}(x)$, areal-valued numerically satisfactory companion of the function ${\rmP}^m_{-\tfrac12+i\tau}(x)$ for $x>1$. In this way, a natural basis for solvingDirichlet problems bounded by conical domains is provided.