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

04/04/2017

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by   T. M. Dunster, et al.

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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 R^m_-1/2+iτ(x), a real-valued numerically satisfactory companion of the function P^m_-12+iτ(x) for x>1. In this way, a natural basis for solving Dirichlet problems bounded by conical domains is provided.