Christoffel transform of classical discrete measures and invariance of determinants of classical and classical discrete polynomials (Q2041723)

The purpose of this paper is to study the Christoffel transform for classical discrete measures and to find a bunch of non trivial determinantal representations in terms of the classical discrete orthogonal polynomials with respect to a certain measure. The polynomials studied in the paper are Hermite, Charlier, Meixner, Laguerre and dual Hahn families. Several new orthogonal polynomials and invariance properties are found by partly using a slightly different normalization from the one used in [\textit{R. Koekoek} et al., Hypergeometric orthogonal polynomials and their \(q\)-analogues. With a foreword by Tom H. Koornwinder. Berlin: Springer (2010; Zbl 1200.33012)]. The proofs use Maya diagrams and Casoration determinants.