On limit relations between some families of bivariate hypergeometric orthogonal polynomials

Abstract

In this paper we deal with limit relations between bivariate hypergeometric polynomials. We analyze the limit relation from trinomial distribution to bivariate Gaussian distribution, obtaining the limit transition from the second-order partial difference equation satisfied by bivariate hypergeometric Kravchuk polynomials to the second-order partial differential equation verified by bivariate hypergeometric Hermite polynomials. As a consequence the limit relation between both families of orthogonal polynomials is established. A similar analysis between bivariate Hahn and bivariate Appell orthogonal polynomials is also presented.