Computations of general Heun functions from their integral series representations
Numerical Analysis
2022-07-07 v2 Numerical Analysis
Mathematical Physics
math.MP
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.
Cite
@article{arxiv.2106.13729,
title = {Computations of general Heun functions from their integral series representations},
author = {Tolga Birkandan and Pierre-Louis Giscard and Aditya Tamar},
journal= {arXiv preprint arXiv:2106.13729},
year = {2022}
}
Comments
Updated with new computations and comparisons with Octave/Matlab performances