Quadratic differentials and asymptotics of Laguerre polynomials with varying complex parameters

DOI10.1016/j.jmaa.2014.02.040zbMath1295.30015arXiv1311.0372OpenAlexW2963297338MaRDI QIDQ402957

Atia, Mohamed Jalel, Andrei Martínez-Finkelshtein, Faouzi Thabet, Pedro Martínez-González

Publication date: 29 August 2014

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.0372

zbMATH Keywords

Riemann-Hilbert problemsgeneralized Laguerre polynomialsstrong and weak asymptoticstrajectories and orthogonal trajectories of a quadratic differential

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Polynomials and rational functions of one complex variable (30C10) Asymptotic representations in the complex plane (30E15)

Related Items (18)

On the existence of short trajectories of quadratic differentials related to generalized Jacobi polynomials with non-real varying parameters ⋮ Uniform asymptotic expansions for Laguerre polynomials and related confluent hypergeometric functions ⋮ Trajectories of quadratic differentials for Jacobi polynomials with complex parameters ⋮ Critical measures for vector energy: global structure of trajectories of quadratic differentials ⋮ Combinatorial description of jumps in spectral networks defined by quadratic differentials ⋮ ON THE EXISTENCE OF FINITE CRITICAL TRAJECTORIES IN A FAMILY OF QUADRATIC DIFFERENTIALS ⋮ Supercritical regime for the kissing polynomials ⋮ Large degree asymptotics of orthogonal polynomials with respect to an oscillatory weight on a bounded interval ⋮ High-order asymptotic expansions of Gaussian quadrature rules with classical and generalized weight functions ⋮ Trajectories of a Quadratic Differential Related to a Particular Algebraic Equation ⋮ Asymptotic root distribution of Charlier polynomials with large negative parameter ⋮ On external fields created by fixed charges ⋮ S-curves in polynomial external fields ⋮ Quadratic differentials (A(z − a)(z − b)/(z − c)2) dz 2 and algebraic Cauchy transform ⋮ Zero distribution of complex orthogonal polynomials with respect to exponential weights ⋮ Critical graph of a polynomial quadratic differential related to a Schrödinger equation with quartic potential ⋮ Asymptotic behavior and zero distribution of polynomials orthogonal with respect to Bessel functions ⋮ Topological recursion and uncoupled BPS structures. I: BPS spectrum and free energies

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