Recurrence Coefficients for Orthogonal Polynomials with a Logarithmic Weight Function

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2024
• Main Authors: Deift, Percy, Piorkowski, Mateusz
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2024
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212119
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Recurrence Coefficients for Orthogonal Polynomials with a Logarithmic Weight Function. Percy Deift and Mateusz Piorkowski. SIGMA 20 (2024), 004, 48 pages

We prove an asymptotic formula for the recurrence coefficients of orthogonal polynomials with orthogonality measure log(2/(1−))d on (−1, 1). The asymptotic formula confirms a special case of a conjecture by Magnus and extends earlier results by Conway and one of the authors. The proof relies on the...