On $q$-deformations of the Heun equation

Understand

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.