\(q\)-difference operators for orthogonal polynomials. (English) Zbl 1185.39005

Ismail, Mourad E. H.; Simeonov, Plamen

J. Comput. Appl. Math. 233, No. 3, 749-761 (2009).

The families of orthogonal polynomials appearing as solutions of Sturm-Liouville differential equations support the operation of two adjoint linear differential operators which respectively raise and lower the degree. A similar theory has been developped for \(q\)-orthogonal polynomials and many results of the “classical” (differential) theory have been extended to the “basic” (\(q\)-analogue) theory, in particular by the authors of the paper reviewed here, which tackles indeterminate moment problems.

Reviewer: Jacques Sauloy (Toulouse)

MSC:

39A13	Difference equations, scaling (\(q\)-differences)
33D45	Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)

Keywords:

\(q\)-difference equations; degree raising and lowering operators; Stieltjes-Wigert; \(q\)-Laguerre; Sturm-Liouville; \(q\)-orthogonal polynomials; indeterminate moment problems

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