Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials - Grandati, Y.; Quesne, C. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
We construct rational extensions of the Darboux-Pöschl-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.