Bi-parametric $su(1,1)$ structure of the Heun class of equations and quasi-polynomial solutions

Abstract

A new bi-parametric $su(1,1)$ algebraization of the Heun class of equations is explored. This yields additional quasi-polynomial solutions of the form $\{z^{\alpha }{P}_N(z):\alpha \in \mathbb{C},N\in {\mathbb{N}}_0\}$ to the General Heun eqaution and its confluent versions. Explicit conditions leading to these quasi-polynomials have been provided for the individual equations to allow direct use. For the Confluent and the Doubly-confluent Heun equations, specific parametric situations leading to (i) an infinite number of quasi-polynomials and (ii) non-algebraizability of the equation have been identified.

Journal info of Ref. 1, Corrected typos

References in corpus (1)

• Quasi-Exact Solvability and Deformations of Sl(2) Algebra