q-difference operators for orthogonal polynomials

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.