An approach to finding the asymptotics of polynomials given by recurrence relations

DOI10.1134/S1061920821020060zbMath1467.42041OpenAlexW3166122242MaRDI QIDQ2037776

S. Yu. Dobrokhotov, Anna V. Tsvetkova

Publication date: 8 July 2021

Published in: Russian Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1061920821020060

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) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Linear difference equations (39A06)

Related Items (4)

Asymptotics of multiple orthogonal Hermite polynomials \(H_{n_1,n_2}(z,\alpha)\) determined by a third-order differential equation ⋮ Plancherel–Rotach type asymptotic formulae for multiple orthogonal Hermite polynomials and recurrence relations ⋮ Global asymptotics for functions of parabolic cylinder and solutions of the Schrödinger equation with a potential in the form of a nonsmooth double well ⋮ Asymptotics of long nonlinear coastal waves in basins with gentle shores

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Lagrangian manifolds related to the asymptotics of Hermite polynomials
• The Pontryagin duality principle for computing a Cherenkov type effect in crystals and difference schemes. II
• Geometry of Lagrangian manifolds and the canonical Maslov operator in complex phase space
• Asymptotic solution of the Cauchy problem for equations with complex characteristics
• Asymptotic expansions for second-order linear difference equations with a turning point
• Efficient formulas for the Maslov canonical operator near a simple caustic
• Asymptotics of wave functions of the stationary Schrödinger equation in the Weyl chamber
• Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model
• Uniform asymptotic solution in the form of an Airy function for semiclassical bound states in one-dimensional and radially symmetric problems
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• Plancherel-Rotach type asymptotics for solutions of linear recurrence relations with rational coefficients
• Complex WKB method for a difference Schrödinger equation with the potential being a trigonometric polynomial
• The leading term of the Plancherel-Rotach asymptotic formula for solutions of recurrence relations
• On polynomials orthogonal on several segments with indefinite weight

This page was built for publication: An approach to finding the asymptotics of polynomials given by recurrence relations