Minimal recurrence relations for connection coefficients between classical orthogonal polynomials: Discrete case

Abstract

We present a simple approach in order to compute recursively the connection coefficients between two families of classical (discrete) orthogonal polynomials (Charlier, Meixner, Kravchuk, Hahn), i.e., the coefficients C m ( n) in the expression P n ( x) = ∑ m=0 n C m ( n) Q m ( x), where { P n ( x)} and { Q m ( x)} belong to the aforementioned class of polynomials. This is done by adapting a general and systematic algorithm, recently developed by the authors, to the discrete classical situation. Moreover, extensions of this method allow to give new addition formulae and to estimate C m ( n)-asymptotics in limit relations between some families.