On a conjecture of A. Magnus concerning the asymptotic behavior of the recurrence coefficients of the generalized Jacobi polynomials

DOI10.1016/j.jat.2009.08.006zbMath1193.42099arXiv0905.2753OpenAlexW1990877773WikidataQ123278360 ScholiaQ123278360MaRDI QIDQ968977

Ana Foulquié Moreno, V. L. Sousa Junior, Andrei Martínez-Finkelshtein

Publication date: 11 May 2010

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.2753

zbMATH Keywords

asymptoticsorthogonal polynomialssteepest descentrecurrence coefficientsgeneralized Jacobi weightsRiemann-Hilbert method

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Riemann-Hilbert problems in context of PDEs (35Q15)

Related Items (13)

On orthogonal polynomials: semiclassical and of second category ⋮ Asymptotics of Muttalib-Borodin determinants with Fisher-Hartwig singularities ⋮ Construction and implementation of asymptotic expansions for Jacobi-type orthogonal polynomials ⋮ Uniform asymptotics of Toeplitz determinants with Fisher-Hartwig singularities ⋮ Asymptotics of orthogonal polynomials for a weight with a jump on \([-1,1\)] ⋮ Toeplitz determinants with merging singularities ⋮ Gaussian integration formulas for logarithmic weights and application to 2-dimensional solid-state lattices ⋮ Asymptotics for Hankel determinants associated to a Hermite weight with a varying discontinuity ⋮ Mehler–Heine formulas for orthogonal polynomials with respect to the modified Jacobi weight ⋮ Asymptotics of Hankel determinants with a Laguerre-type or Jacobi-type potential and Fisher-Hartwig singularities ⋮ Asymptotic behavior and zero distribution of polynomials orthogonal with respect to Bessel functions ⋮ Painlevé XXXIV Asymptotics of Orthogonal Polynomials for the Gaussian Weight with a Jump at the Edge ⋮ Pointwise asymptotics of the ratio of Jacobi-type polynomials

Cites Work

• Asymptotics of Toeplitz, Hankel, and Toeplitz+Hankel determinants with Fisher-Hartwig singularities
• The isomonodromy approach to matrix models in 2D quantum gravity
• Strong asymptotics of the recurrence coefficients of orthogonal polynomials associated to the generalized Jacobi weight.
• On the distribution of the length of the second row of a Young diagram under Plancherel measure
• The Riemann--Hilbert approach to strong asymptotics for orthogonal polynomials on [-1,1]
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• Hankel determinant and orthogonal polynomials for the Gaussian weight with a jump
• Asymptotics for the painlevé II equation
• Infinite random matrices and ergodic measures
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