On q-Deformations of the Heun Equation
Copyright policy )On q-Deformations of the Heun Equation
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.
- Chuo University Japan
Lamé, Mathieu, and spheroidal wave functions, Difference equations, scaling (\(q\)-differences), quasi-exact solvability, degeneration, FOS: Physical sciences, Mathematical Physics (math-ph), 39A13, 33E10, regular singularity, Mathematics - Classical Analysis and ODEs, Heun equation, Classical Analysis and ODEs (math.CA), FOS: Mathematics, \(q\)-deformation, Applications of difference equations, Mathematical Physics
Lamé, Mathieu, and spheroidal wave functions, Difference equations, scaling (\(q\)-differences), quasi-exact solvability, degeneration, FOS: Physical sciences, Mathematical Physics (math-ph), 39A13, 33E10, regular singularity, Mathematics - Classical Analysis and ODEs, Heun equation, Classical Analysis and ODEs (math.CA), FOS: Mathematics, \(q\)-deformation, Applications of difference equations, Mathematical Physics
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