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arXiv · 2410.05003

$m$-step rational extensions of the trigonometric Darboux-P\"{o}schl-Teller potential based on para-Jacobi polynomials

Yves Grandati·Christiane Quesne
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Abstract

A previous construction of regular rational extensions of the trigonometric Darboux-P\"oschl-Teller potential, obtained by one-step Darboux transformations using seed functions associated with the para-Jacobi polynomials of Calogero and Yi, is generalized by considering $m$-step Darboux transformations. As a result, some novel families of exceptional orthogonal polynomials depending on $m$ discrete parameters, as well as $m$ continuous real ones $\lambda_1$, $\lambda_2$, \ldots, $\lambda_m$, are obtained. The restrictions imposed on these parameters by the rational extensions regularity conditions are studied in detail.

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Yves Grandati, Christiane Quesne. 2024-10-07. $m$-step rational extensions of the trigonometric Darboux-P\"{o}schl-Teller potential based on para-Jacobi polynomials. https://arxiv.org/abs/2410.05003

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