On zeros of polynomials associated with Heun class equations
Classical Analysis and ODEs
2025-10-27 v3 Mathematical Physics
math.MP
Abstract
Sch\"afke and Schmidt established that the asymptotics of the coefficients of the local solution to some linear differential equation is related to global structures of solutions. The Heun class equations have the accessory parameters, and we investigate the polynomials whose variable is the accessory parameter which appears as the coefficients of the local solution. By calculating the zeros of the polynomials numerically, we obtain the data of the spectral related to the Heun class equations numerically.
Cite
@article{arxiv.2503.10355,
title = {On zeros of polynomials associated with Heun class equations},
author = {Mizuki Mori and Kouichi Takemura},
journal= {arXiv preprint arXiv:2503.10355},
year = {2025}
}
Comments
23 pages, a proof of Proposition 4.8 was added