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Álvarez-Nodarse, R.

On characterizations of classical polynomials. (English) Zbl 1108.33008

J. Comput. Appl. Math. 196, No. 1, 320-337 (2006).
The author presents a unified study of the classical discrete polynomials and \(q\)-polynomials of the \(q\)-Hahn tableau by using the difference calculus on linear-type lattices. He obtains several characterization theorems for the classical discrete and \(q\)-polynomials of the \(q\)-Hahn tableau. The classical continuous case can be obtained from the \(q\)-case by taking the limit \(q\leftarrow 1^{-}\). He also discusses some problems related to the characterization by F. Marcellán et al. [Acta Appl. Math. 34, 283–303 (1994; Zbl 0793.33009)].
Reviewer: Youssef Ben Cheikh (Monastir)

Cited in 43 Documents

MSC:

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)

Keywords:

classical polynomials; q-Hahn tableau; discrete polynomials

Citations:

Zbl 0793.33009
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Full Text: DOI

References:

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