q-Coherent pairs and q-orthogonal polynomials

26 pages, no figures.-- MSC2000 codes: 33D45, 33D15.MR#: MR1891019 (2003d:33038)Zbl#: Zbl 1020.33005In this paper we introduce the concept of q-coherent pair of linear functionals. We prove that if (u0,u1) is a q-coherent pair of linear functionals, then at least one of them has to be a q-classical linear functional. Moreover, we present the classification of all q-coherent pairs of positive-definite linear functionals when u0 or u1 is either the little q-Jacobi linear functional or the little q-Laguerre/Wall linear functional. Finally, by using limit processes, we recover the classification of coherent pairs of linear functionals stated by Meijer.E. Godoy wishes to acknowledge partial financial support by Dirección General de Enseñanza Superior (DGES) of Spain under grant PB-96-0952. The research of F. Marcellán has been partially supported by DGES of Spain under Grant PB96-0120-C03-01 and INTAS Project 2000-272.Publicad