Extended Krein-Adler theorem for the translationally shape invariant potentials

Abstract

Considering successive extensions of primary translationally shape invariant potentials, we enlarge the Krein-Adler theorem to mixed chains of state adding and state-deleting Darboux-Backlund transformations. It allows us to establish novel bi-linear Wronskian and determinantal identities for classical orthogonal polynomials.