On the q-polynomials in the exponential lattice x(s) = c1qs+c3

The main goal of this paper is to continue the study of the q-polynomials on non-uniform lattices by using the approach introduced by Nikiforov and Uvarov in 1983. We consider the q-polynomials on the non-uniform exponential lattice x(s) = c(1)q(s) + c(3) and study some of their properties (differentiation formulas, structure relations, representation in terms of hypergeo metric and basic hypergeometric functions, etc). Special emphasis is given to p-analogues of the Charlier orthogonal polynomials. For these polynomials (Charlier) we compute the main data, i.e., the coefficients of the three-term recurrence relation, 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.