Polynomial solutions of q-Heun equation and ultradiscrete limit. Issue 5 (4th May 2019)

• Record Type: Journal Article
• Authors: Kojima, Kentaro; Sato, Tsukasa; Takemura, Kouichi
• Is Part Of: Journal of difference equations and applications. Volume 25:Issue 5(2019)
• Page Start: 647
• Page End: 664
• Publication Date: 2019-05-04
• Subjects: q-Heun equation -- polynomial solution -- ultradiscrete limit -- q-difference equation -- Heun equation -- Ruijsenaars system; 39A13 -- 33E10 -- 30C15; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2019.1619709
• Languages: English
• ISSNs: 1023-6198

Abstract

ABSTRACT: 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.