An improved algorithm and a Fortran 90 module for computing the conical function P − 1 / 2 + i τ m ( x )

Abstract In this paper we describe an algorithm and a Fortran 90 module (Conical) for the computation of the conical function P-12+iτm(x) for x>-1, m≥0, τ>0. These functions appear in the solution of Dirichlet problems for domains bounded by cones; because of this, they are involved in a large number of applications in engineering and physics. In the Fortran 90 module, the admissible parameter ranges for computing the conical functions in standard IEEE double precision arithmetic are restricted to (x,... Title of program: Conical Catalogue Id: AELD_v1_0 Nature of problem Conical functions appear in a large number of applications because these functions are the natural function basis for solving Dirichlet problems bounded by conical domains. Also, they are the Kernel of the Mehler-Fock transform. Versions of this program held in the CPC repository in Mendeley Data AELD_v1_0; Conical; 10.1016/j.cpc.2011.11.025 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)