Heun's differential equation and its q-deformation

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.

6 pages

References in corpus (6)

• Nonlinear Effective Theory of Dark Energy
• Degenerations of Ruijsenaars-van Diejen operator and q-Painleve equations
• On $q$-deformations of the Heun equation
• Real-root property of the spectral polynomial of the Treibich-Verdier potential and related problems
• Polynomial solutions of $q$-Heun equation and ultradiscrete limit
• Ultradiscrete limit of the spectral polynomial of the $q$-Heun equation

Cited by in corpus (1)

• Diagonalization of the Heun-Askey-Wilson operator, Leonard pairs and the algebraic Bethe ansatz