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Dobrogowska, Alina; Odzijewicz, Anatol

Second order \(q\)-difference equations solvable by factorization method. (English) Zbl 1119.39017

J. Comput. Appl. Math. 193, No. 1, 319-346 (2006).
The factorization method to solve ordinary differential equations due to Darboux has many applications to orthogonal polynomials and quantum mechanics. The authors propose an extension to \(q\)-difference equations. It is a \(q\)-analogue, since, in the continuous limit \(q \to 1\), it boils down to the classical factorization method (at least in the usual intuitive description of “continuous limit”). The paper contains the proof in a particular important case (indeed, a generalisation of a famous study by L. Infeld and T. E. Hull, Rev. Mod. Phys. 23, 21–68 (1951; Zbl 0043.38602) that the \(q\)-Hahn orthogonal polynomials are among the solutions. They also consider other interesting examples.
Reviewer: Jacques Sauloy (Toulouse)

Cited in 44 Documents

MSC:

39A13 Difference equations, scaling (\(q\)-differences)
33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)
39A12 Discrete version of topics in analysis

Keywords:

discretization; \(q\)-Hahn orthogonal polynomials

Citations:

Zbl 0043.38602
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\textit{A. Dobrogowska} and \textit{A. Odzijewicz}, J. Comput. Appl. Math. 193, No. 1, 319--346 (2006; Zbl 1119.39017)
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