THE RAMANUJAN JOURNAL, Vol. 3, No. 1 (1999), 83-89.

Finite differences and orthogonal polynomials

CHU WENCHANG
9 Rue Du Regard, 75006 Paris, France
chu.dicastro@wanadoo.fr

Received June 2, 1997; Accepted February 3, 1998

Abstract. By combining finite differences with symmetric functions, we present an elementary demonstration for the limit relation from Laguerre to Hermite polynomials, proposed by Richard Askey. Another limit relation between these two polynomials will also be established.

Keywords: Hermite polynomials, Laguerre polynomials, limit relation, finite difference, symmetric function

1991 Mathematics Classification: Primary 33C45; Secondary 05E05