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).