Laurent Biorthogonal Polynomials and Riordan Arrays

2013/11/10 by Paul Barry, Barry, Paul
Mathematics · #11B83 #11C20 #15B36 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1311.2292

openalex publication_date 2013/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that Laurent biorthogonal polynomials whose defining three-term recurrence have constant coefficients have coefficient arrays that are Riordan arrays. For each such family of Laurent biorthogonal polynomials we associate in a natural way a family of orthogonal polynomials. We also extend these results to a notion of generalized orthogonal polynomials whose recurrence depends on three parameters.

Citations

• On Some Alternative Characterizations of Riordan Arrays

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