A characterization theorem for semi-classical orthogonal polynomials on non-uniform lattices

A. Branquinho, Y. Chen, G. Filipuk and M.N. Rebocho

Applied Mathematics and Computation, 2018, vol. 334, issue C, 356-366

Abstract: It is proved a characterization theorem for semi-classical orthogonal polynomials on non-uniform lattices that states the equivalence between the Pearson equation for the weight and some systems involving the orthogonal polynomials as well as the functions of the second kind. As a consequence, it is deduced the analogue of the so-called compatibility conditions in the ladder operator scheme. The classical orthogonal polynomials on non-uniform lattices are then recovered under such compatibility conditions, through a closed formula for the recurrence relation coefficients.

Keywords: Orthogonal polynomials; Divided-difference operator; Non-uniform lattices; Askey–Wilson operator; Semi-classical class (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:334:y:2018:i:c:p:356-366

DOI: 10.1016/j.amc.2018.04.022

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