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arXiv · 2003.10075

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

Priyasri Kar
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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.

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BibTeXRIS

Priyasri Kar. 2020-03-23. Bi-parametric $su(1,1)$ structure of the Heun class of equations and quasi-polynomial solutions. https://arxiv.org/abs/2003.10075

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