Lima, Helder, Loureiro, Ana F. (2022) Multiple orthogonal polynomials with respect to Gauss' hypergeometric function. Studies in Applied Mathematics, 148 (1). pp. 154185. ISSN 00222526. (doi:10.1111/sapm.12437) (KAR id:85292)
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Official URL: https://doi.org/10.1111/sapm.12437 
Abstract
A new set of multiple orthogonal polynomials of both type I and type II with respect to two weight functions involving Gauss' hypergeometric function on the interval (0,1) is studied. This type of polynomials has direct applications in the investigation of singular values of products of Ginibre random matrices and are connected with branched continued fractions and totalpositivity problems in combinatorics. The pair of orthogonality measures is shown to be a Nikishin system and to satisfy a matrix Pearsontype differential equation. The focus is on the polynomials whose indices lie on the stepline, for which it is shown that the differentiation gives a shift in the parameters, therefore satisfying Hahn's property. We obtain Rodriguestype formulas for type I polynomials and functions, while a more detailed characterization is given for the type II polynomials (aka 2orthogonal polynomials) that include an explicit expression as a terminating hypergeometric series, a thirdorder differential equation, and a thirdorder recurrence relation. The asymptotic behavior of their recurrence coefficients mimics those of Jacobi–Piñeiro polynomials, based on which their asymptotic zero distribution and a Mehler–Heine asymptotic formula near the origin are given. Particular choices of the parameters and confluence relations give some known systems such as special cases of the Jacobi–Piñeiro polynomials, Jacobitype 2orthogonal polynomials, components of the cubic decomposition of threefold symmetric Hahnclassical polynomials, and multiple orthogonal polynomials with respect to confluent hypergeometric functions of the second kind.
Item Type:  Article 

DOI/Identification number:  10.1111/sapm.12437 
Uncontrolled keywords:  Multiple orthogonal polynomials, Gauss hypergeometric function, Nikishin system, Rodriguestype formula, generalised hypergeometric series, 2orthogonal polynomials, Hahn classical 
Subjects: 
Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus Q Science > QA Mathematics (inc Computing science) > QA351 Special functions 
Divisions:  Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science 
Depositing User:  Ana F. Loureiro 
Date Deposited:  04 Jan 2021 01:06 UTC 
Last Modified:  22 Feb 2022 15:32 UTC 
Resource URI:  https://kar.kent.ac.uk/id/eprint/85292 (The current URI for this page, for reference purposes) 
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