TY - JOUR
T1 - Second-Order Difference Equation for Sobolev-Type Orthogonal Polynomials. Part II: Computational Tools
AU - Filipuk , Galina
AU - Mañas-Mañas , Juan F.
AU - Moreno-Balcázar , Juan J.
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 960
EP - 979
PY - 2023
DA - 2023/10
SN - 13
DO - http://doi.org/10.4208/eajam.2022-235.190223
UR - https://global-sci.org/intro/article_detail/eajam/22070.html
KW - Sobolev orthogonal polynomials, second-order difference equation, symbolic computation.
AB - <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>