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arXiv · 1712.09564

On $q$-deformations of the Heun equation

Kouichi Takemura
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Abstract

The $q$-Heun equation and its variants arise as degenerations of Ruijsenaars-van Diejen operators with one particle. We investigate local properties of these equations. In particular we characterize the variants of the $q$-Heun equation by using analysis of regular singularities. We also consider the quasi-exact solvability of the $q$-Heun equation and its variants. Namely we investigate finite-dimensional subspaces which are invariant under the action of the $q$-Heun operator or variants of the $q$-Heun operator.

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Kouichi Takemura. 2017-12-27. On $q$-deformations of the Heun equation. https://doi.org/10.3842/sigma.2018.061

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