A combinatorial formula for the linearization coefficients of general Sheffer polynomials

Abstract

We prove a formula for the linearization coefficients of the general Sheffer polynomials, which unifies all the special known results for Hermite, Charlier, Laguerre, Meixner and Meixner-Pollaczek polynomials. Furthermore, we give a new and explicit real Version of the corresponding formula for Meiwner-Pollaczek polynomials. Our proof is based on some explicit bijections and sign-reversing weight-preserving involutions. (C) 2001 Academic Press.