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ABSTRACT
A general approach to the study of orthogonal polynomials related to Sobolev inner products which are defined in terms of divided-difference operators having the fundamental property of leaving a polynomial of degree n−1 when applied to a polynomial of degree n is presented. This paper gives analytic properties for the orthogonal polynomials, including the second-order holonomic difference equation satisfied by them.
Acknowledgements
The author thanks the anonymous reviewer of this paper for very carefully reading the manuscript, and also for her/his valuable comments and suggestions for improving the paper significantly.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Funding
This work was partially supported by the Centre for Mathematics of the University of Coimbra – UID/MAT/00324/2019, funded by the Portuguese Government through FCT/MCTES and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020.