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

Abstract

Conical functions appear in a large number of applications in physics and engineering. In this paper we describe an extension of our module CONICAL for the computation of conical functions. Specifically, the module includes now a routine for computing the function ${\mathrm{R}}_{-\frac{1}{2}+i\tau }^m(x)$, a real-valued numerically satisfactory companion of the function ${\mathrm{P}}_{-\frac{1}{2}+i\tau }^m(x)$ for $x>1$. In this way, a natural basis for solving Dirichlet problems bounded by conical domains is provided.

To appear in Computer Physics Communications

References in corpus (3)

• GammaCHI: a package for the inversion and computation of the gamma and chi-square cumulative distribution functions (central and noncentral)
• An improved algorithm and a Fortran 90 module for computing the conical function $P_{-1/2+i\tau }^m(x)$
• Computation of a numerically satisfactory pair of solutions of the differential equation for conical functions of non-negative integer orders