Wronskian and Casorati determinant representations for Darboux–Pöschl–Teller potentials and their difference extensions

We consider some special reductions of generic Darboux?Crum dressing formulae and of their difference versions. As a matter of fact, we obtain some new formulae for Darboux?P?schl?Teller (DPT) potentials by means of Wronskian determinants. For their difference deformations (called DDPT-I and DDPT-II potentials) and the related eigenfunctions, we obtain new formulae described by the ratios of Casorati determinants given by the functional difference generalization of the Darboux?Crum dressing formula.