Work

Strong asymptotics for Jacobi-Piñeiro orthogonal polynomials

Year: 2026

Type: preprint

Abstract: We investigate the asymptotic behavior of Jacobi-Piñeiro polynomials of degree $2n$ orthogonal on $[0,1]$ with respect to weights $w_j(x) = x^{α_j}(1-x)^β$, $j=1,2$ where $α_1,α_2, β>-1$, and $α_1-α_2 \notin \mathbb{Z}$. These polynomials are characterized by a Riemann-Hilbert problem for a $3 \times 3$ matrix-valued function. We use the Deift-Zhou steepest descent method for Riemann-Hilbert problems to obtain strong uniform asymptotics in the complex plane. The local parametrix around the origin is constructed using Meijer G-functions. We match the local parametrix around the origin with the global parametrix with a double matching, a technique that was recently introduced.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.20594

Authors: Kalmykov, Sergei, Lysov, Vladimir, Shukla, Vinay

Institutions: Russian Academy of Sciences, Keldysh Institute of Applied Mathematics, Shanghai Jiao Tong University, Bennett University

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Far East Branch, Russian Academy of Sciences

OpenAlex ID: W7204093102

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