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On the second-order holonomic equation for Sobolev-type orthogonal polynomials. (English) Zbl 1506.33011

Summary: 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.

MSC:

33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)
42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis

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