An improved algorithm and a Fortran 90 module for computing the conical function image Original Research Article

In this paper we describe an algorithm and a Fortran 90 module (Conical) for the computation of the conical function image for image, image, image. 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 image and image. Based on tests of the three-term recurrence relation satisfied by these functions and direct comparison with Maple, we claim a relative accuracy close to image in the full parameter range, although a mild loss of accuracy can be found at some points of the oscillatory region of the conical functions. The relative accuracy increases to image in the region of the monotonic regime of the functions where integral representations are computed (image)