Ladder operators for \(q\)-orthogonal polynomials
The authors construct the \(q\)-difference analog of the ladder operators for orthogonal polynomials related to a class of indeterminate moment problem. A general theorem is proved giving auxiliary relations to define the so-called lowering and rasing operators for polynomials which are orthogonal with respect to absolutely continuous measures. In particular, the Stieltjes-Wigert and \(q\)-Laguerre polynomials are investigated.
orthogonal polynomials and their \(q\)-analogues
scientific article