Four-term recurrences, orthogonal polynomials and Riordan arrays

Barry, Paul and Hennessy, Aoife (2012) Four-term recurrences, orthogonal polynomials and Riordan arrays. Journal of Integer Sequences, 15. 12.4.2. ISSN 1530-7638

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We study constant coefficient four term recurrences for polynomials, in analogy to the three-term recurrences that are associated with orthogonal polynomials. We show that for a family of polynomials obeying such a four-term recurrence, the coefficient array is an ordinary Riordan array of a special type, and vice versa. In certain cases, it is possible to transform these polynomials into related orthogonal polynomials. We characterize the form of the production matrices of the inverse coefficient arrays.

Item Type: Article
Departments or Groups: *NONE OF THESE*
Divisions: School of Science
Depositing User: Paul Barry
Date Deposited: 19 Nov 2012 15:45
Last Modified: 22 Aug 2016 10:26

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