Polynomial solutions of q-Heun equation and ultradiscrete limit |
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Authors: | Kentaro Kojima Tsukasa Sato |
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Institution: | Department of Mathematics, Faculty of Science and Engineering, Chuo University, Tokyo, Japan |
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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. |
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Keywords: | q-Heun equation polynomial solution ultradiscrete limit q-difference equation Heun equation Ruijsenaars system |
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