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Generalization of rational extensions produces novel orthogonal polynomials in exceptional families, indicating deeper parameter constraints.
A previous construction of regular rational extensions of the trigonometric Darboux-Pöschl-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 λ1, λ2, …, λm, are obtained. The restrictions imposed on these parameters by the rational extensions regularity conditions are studied in detail.
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Grandati et al. (2025) studied this question.
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