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arXiv · 2006.14391

Ladder operators and a second--order difference equation for general discrete Sobolev orthogonal polynomials

Galina Filipuk·Juan F. Mañas-Mañas·Juan J. Moreno-Balcázar
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Abstract

We consider a general discrete Sobolev inner product involving the Hahn difference operator, so this includes the well--known difference operators $\mathscr{D}_{q}$ and $\Delta$ and, as a limit case, the derivative operator. The objective is twofold. On the one hand, we construct the ladder operators for the corresponding nonstandard orthogonal polynomials and we obtain the second--order difference equation satisfied by these polynomials. On the other hand, we generalise some related results appeared in the literature as we are working in a more general framework. Moreover, we will show that all the functions involved in these constructions can be computed explicitly.

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Galina Filipuk, Juan F. Mañas-Mañas, Juan J. Moreno-Balcázar. 2020-06-25. Ladder operators and a second--order difference equation for general discrete Sobolev orthogonal polynomials. https://doi.org/10.1080/10236198.2022.2103412

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