Abstract
The main goal of this paper is to continue the sutudy 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 qs +c 3 and study some of their properties (differentiation formulas, structure relations, represntation in terms of hypergeometric and basic hypergeometric functions, etc). Special emphasis is given to q-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 , respectively.
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