Polynomial solutions of $q$-Heun equation and ultradiscrete limit

Autor:	Kojima, Kentaro, Sato, Tsukasa, Takemura, Kouichi
Rok vydání:	2018
Předmět:	Mathematics - Classical Analysis and ODEs Mathematical Physics Mathematics - Quantum Algebra 39A13 33E10 30C15
Zdroj:	Journal of Difference Equations and Applications 25 (2019) 647-664
Druh dokumentu:	Working Paper
DOI:	10.1080/10236198.2019.1619709
Popis:	We study polynomial-type solutions of the $q$-Heun equation, which is related with quasi-exact solvability. The condition that the $q$-Heun equation has a non-zero polynomial-type solution is described by the roots of the spectral polynomial, whose variable is the accessory parameter $E$. We obtain sufficient conditions that the roots of the spectral polynomial are all real and distinct. We consider the ultradiscrete limit to clarify the roots of the spectral polynomial and the zeros of the polynomial-type solution of the $q$-Heun equation. Comment: 17 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1809.01428 Zobrazit plný text záznamu View this record from Arxiv