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)= ∑ n m=0 C m(n)Q m(x) , where P n ( x) and Q m ( x) belong to the aforementioned class of polynomials. This is SCV2 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.