Difference Operator of Infinite Order with Sobolev-Type Charlier Polynomials asEigenfunctions

摘要

Polynomials are considered which are orthogonal with respect to the inner product< f,g > = Summation, x = 0 to x = infinity, of f(x)g(x)(e(sup -alpha))(alpha (sup x))/(x factorial) + (lambda)f(0)g(0) + (mu)(Delta)f(0)(Delta)g(0), alpha > 0, lambda = or > 0, mu = or > 0. A representation for these polynomials is presented. It is shown that in the case lambda = 0 and mu > 0 these polynomials are eigenfunctions of a difference operator of infinite order. A formula for the eigenvalues and a representation for the coefficients in the differential operator are presented. (Copyright (c) 1994 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)