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Heun's differential equation and its q-deformation (1903.02415v1)

Published 6 Mar 2019 in math.CA, math-ph, and math.MP

Abstract: The $q$-Heun equation is a $q$-difference analogue of Heun's differential equation. We review several solutions of Heun's differential equation and investigate polynomial-type solutions of $q$-Heun equation. The limit $q\to 1$ corresponding to Heun's differential equation and the ultradiscrete limit $q\to 0$ are considered.