@Article{EAJAM-13-4,
author = {Galina, Filipuk and Mañas-Mañas, Juan, F. and Moreno-Balcázar, Juan, J.},
title = {Second-Order Difference Equation for Sobolev-Type Orthogonal Polynomials. Part II: Computational Tools},
journal = {East Asian Journal on Applied Mathematics},
year = {2023},
volume = {13},
number = {4},
pages = {960--979},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.2022-235.190223},
url = {https://global-sci.com/article/82447/second-order-difference-equation-for-sobolev-type-orthogonal-polynomials-part-ii-computational-tools}
}