English

On the derivatives of the Heun functions

Classical Analysis and ODEs 2020-09-10 v2 Mathematical Physics math.MP

Abstract

The Heun functions satisfy linear ordinary differential equations of second order with certain singularities in the complex plane. The first order derivatives of the Heun functions satisfy linear second order differential equations with one more singularity. In this paper we compare these equations with linear differential equations isomonodromy deformations of which are described by the Painlev\'e equations PIIPVIP_{II}-P_{VI}.

Keywords

Cite

@article{arxiv.1907.12692,
  title  = {On the derivatives of the Heun functions},
  author = {G. Filipuk and A. Ishkhanyan and J. Dereziński},
  journal= {arXiv preprint arXiv:1907.12692},
  year   = {2020}
}