On the q-polynomials in the exponential lattice $x(s)=c_1q +c_3$

26 pages, no figures.-- MSC1991 code: 33D25.MR#: MR1771452 (2001b:33022)Zbl#: Zbl 0956.33009^aThe main goal of this paper is to continue the study of q-polynomials on non-uniform lattices by using the approach introduced by A. F. Nikiforov and V. B. Uvarov [Akad. Nauk SSSR Inst. Prikl. Mat. Preprint 1983, no. 17, 34 pp.; MR0753537 (86c:39006)]. We consider the q-polynomials on the non-uniform exponential lattice $x(s)=c_1q^s+c_3$ and study some of their properties (differentiation formulas, structure relations, representation in terms of hypergeometric and basic hypergeometric functions, etc.). Special emphasis is given to q-analogues of the Charlier orthogonal polynomials. For these Charlier polynomials we compute the main data, i.e., the coefficients of the three-term recurrence relation, the structure relation, the square of the norm, etc., in the exponential lattices $x(s)=q^s$ and $x(s)=(q^s-1)/(q-1)$, respectively.This work was completed while one of the authors (RAN) was visiting the Universidade de Coimbra. He is very grateful to the Department of Mathematics of Universidade de Coimbra for the kind hospitality and the Centro de Matematica da Universidade de Coimbra for financial support. The research of the authors was partially supported by Dirección General de Enseñanza Superior (DGES) PB 96-0120-C03-01 and the European project INTAS 93-219-ext.Publicad