q-difference operators for orthogonal polynomials

摘要

In this work we apply a q-ladder operator approach to orthogonal polynomials arising from a class of indeterminate moment problems. We derive general representation of first and second order q-difference operators and we study the solution basis of the corresponding second order q-difference equations and its properties. The results are applied to the Stieltjes–Wigert and the q-Laguerre polynomials.