On the Properties for Modifications of Classical Orthogonal Polynomials of Discrete Variables.1

We consider a modiication of moment functionals for some classical polynomials of a discrete variable by adding a mass point at x = 0. We obtain the resulting orthogonal polynomials, identify them as hypergeometric functions and derive the second order diierence equation which these polynomials satisfy. The corresponding tridiagonal matrices and associated polynomials were also studied. x1 Introduction. The study of orthogonal polynomials with respect to a modiication of a linear functional in the linear space of polynomials with real coeecients via the addition of one or two delta Dirac measures has been performed by several authors. In particular, Chihara 5] has considered some properties of such polynomials in terms of the location of the mass point with respect to the support of a positive measure. More recently Marcelll an and Maroni 10] analyzed a more general situation for regular (quasi-deenite) linear functionals, i.e., such that the principal submatrices of the corresponding innnite Hankel matrices associated with the moment sequences are nonsingular. A special emphasis is given to the modiications of classical linear functionals (Hermite, Laguerre, Jacobi and Bessel). Koornwinder 9] considered a system of polynomials orthogonal with respect to the classical weigtht function for Jacobi polynomials with two extra point masses added at x = 1 and x = 1. For generalized Laguerre polynomials fL ;A n (x)g 1 n=0 that are orthogonal on 0; 1) with respect to the linear functional C on the linear space of polynomials with real coeecients deened as