Computations of general Heun functions from their integral series representations

T. Birkandan (1) , P.-L Giscard (2) , A. Tamar

1 İstanbul Teknik Üniversitesi, Fizik Mühendisliği
2 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

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.

Mots clés: Heun function; Path-sum

Domaines: Combinatoire [math.CO]; Systèmes dynamiques [math.DS]; Physique mathématique [math-ph]; Physique [physics]; Physique mathématique [math-ph]

T. Birkandan, P.-L Giscard, A. Tamar. Computations of general Heun functions from their integral series representations. Days on Diffraction (DD) 2021, May 2021, St.Petersburg, Russia. pp.12-18, ⟨10.1109/DD52349.2021.9598600⟩. ⟨hal-03597176⟩