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Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials

Abstract : We construct rational extensions of the Darboux-Poschl-Teller and isotonic potentials via two-step confluent Darboux transformations. The former are strictly isospectral to the initial potential, whereas the latter are only quasi-isospectral. Both are associated to new families of orthogonal polynomials, which, in the first case, depend on a continuous parameter. We also prove that these extended potentials possess an enlarged shape invariance property.
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Yves Grandati, Christiane Quesne. Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials. Symmetry, Integrability and Geometry : Methods and Applications, National Academy of Science of Ukraine, 2015, 11, pp.061. ⟨10.3842/SIGMA.2015.061⟩. ⟨hal-01513175⟩

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