Computations of general Heun functions from their integral series representations

Abstract

We present a numerical implementation of the recently developed unconditionally convergent representation of general Heun functions as integral series. We produce two codes in Python available for download, one of which is especially aimed at reproducing the output of Mathematica's HeunG function. We show that the present code compares favorably with Mathematica's HeunG and with an Octave/Matlab code of Motygin, in particular when the Heun function is to be evaluated at a large number of points if less accuracy is sufficient. We suggest further improvements concerning the accuracy and discuss the issue of singularities.

arXiv commentUpdated with new computations and comparisons with Octave/Matlab performances

References in corpus (9)

• The Magnus expansion and some of its applications
• Heun Functions and Some of Their Applications in Physics
• Schrödinger potentials solvable in terms of the general Heun functions
• An Exact Formulation of the Time-Ordered Exponential using Path-Sums
• Quantum Field Theory Applications of Heun Type Functions
• On evaluation of the Heun functions
• Tridiagonalization of systems of coupled linear differential equations with variable coefficients by a Lanczos-like method
• Elementary Integral Series for Heun Functions. With an Application to Black-Hole Perturbation Theory
• Lanczos-like algorithm for the time-ordered exponential: The $\ast$-inverse problem

Cited by in corpus (1)

• Symbolic analysis of second-order ordinary differential equations with polynomial coefficients