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

2020/03/23 by Priyasri Kar, Kar, Priyasri
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2003.10075

openalex publication_date 2020/03/23 · openalex created_date 2020/03/27 · openalex updated_date 2026/07/28

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^αP_N(z): α∈ ℂ, N ∈ ℕ₀\ 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.

Citations

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

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