East Asian J. Appl. Math., 13 (2023), pp. 960-979.
Published online: 2023-10
Cited by
- BibTex
- RIS
- TXT
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.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2022-235.190223}, url = {http://global-sci.org/intro/article_detail/eajam/22070.html} }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.