Results for some inversion problems for classical continuous and discrete orthogonal polynomials

Abstract

Explicit expressions for the coefficients in the expansion of classical discrete orthogonal polynomials (Charlier, Meixner, Krawtchouck, Hahn, Hahn - Eberlein) into the falling factorial basis are given. The corresponding inversion problems are solved explicitly. This is done by using a general algorithm, recently developed by the authors, which is also applied to this kind of inversion problem but relating the basis and the classical (continuous) orthogonal polynomials of Jacobi, Laguerre, Hermite and Bessel.