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

Rebocho, M. N.; Filipuk, Galina; Chen, Yang; Branquinho, A.

http://hdl.handle.net/10400.6/8996

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Abstract(s)

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

URI

http://hdl.handle.net/10400.6/8996

Citation

A. Branquinho, Y. Chen, G. Filipuk, and M.N. Rebocho, A characterization theorem for semi-classical orthogonal polynomials on non-uniform lattices, Applied Mathematics and Computation 334 (2018) 356-366