Second-Order Difference Equation for Sobolev-Type Orthogonal Polynomials. Part II: Computational Tools
Year: 2023
Author: Galina Filipuk, Juan F. Mañas-Mañas, Juan J. Moreno-Balcázar
East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 4 : pp. 960–979
Abstract
We consider polynomials orthogonal with respect to a nonstandard inner product. In fact, we deal with Sobolev-type orthogonal polynomials in the broad sense of the expression. This means that the inner product under consideration involves the Hahn difference operator, thus including the difference operators $\mathscr{D}_q$ and $∆$ and, as a limit case, the derivative operator. In a previous work, we studied properties of these polynomials from a theoretical point of view. There, we obtained a second-order differential/difference equation satisfied by these polynomials. The aim of this paper is to present an algorithm and a symbolic computer program that provides us with the coefficients of the second-order differential/difference equation in this general context. To illustrate both, the algorithm and the program, we will show three examples related to different operators.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.2022-235.190223
East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 4 : pp. 960–979
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Sobolev orthogonal polynomials second-order difference equation symbolic computation.