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Three-fold symmetric Hahn-classical multiple orthogonal polynomials

Loureiro, Ana F., Van Assche, Walter (2019) Three-fold symmetric Hahn-classical multiple orthogonal polynomials. Analysis and Applications, 18 (2). pp. 271-332. ISSN 0219-5305. (doi:10.1142/S0219530519500106) (KAR id:76811)


We characterize all the multiple orthogonal three-fold symmetric polynomial sequences whose sequence of derivatives is also multiple orthogonal. Such a property is commonly called the Hahn property and it is an extension of the concept of classical polynomials to the context of multiple orthogonality. The emphasis is on the polynomials whose indices lie on the step line, also known as 2-orthogonal polynomials. We explain the relation of the asymptotic behavior of the recurrence coefficients to that of the largest zero (in absolute value) of the polynomial set. We provide a full characterization of the Hahn-classical orthogonality measures supported on a 3-star in the complex plane containing all the zeros of the polynomials. There are essentially three distinct families, one of them 2-orthogonal with respect to two confluent functions of the second kind. This paper complements earlier research of Douak and Maroni.

Item Type: Article
DOI/Identification number: 10.1142/S0219530519500106
Uncontrolled keywords: Orthogonal polynomials, multiple orthogonal polynomials, confluent hypergeometric function, Airy function, Hahn classical polynomials, recurrence relation, linear differential equation
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Ana F. Loureiro
Date Deposited: 26 Sep 2019 09:21 UTC
Last Modified: 08 Dec 2022 23:45 UTC
Resource URI: (The current URI for this page, for reference purposes)

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