Orthogonal polynomials, asymptotics, and Heun equations

DOI10.1063/1.5102102zbMath1427.42031arXiv1905.04869OpenAlexW2985444737WikidataQ126841313 ScholiaQ126841313MaRDI QIDQ5206045

Longjun Zhan, Yang Chen, Galina Filipuk

Publication date: 17 December 2019

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

Full work available at URL: https://arxiv.org/abs/1905.04869

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Moment problems and interpolation problems in the complex plane (30E05) Classical hypergeometric functions, ({}_2F_1) (33C05) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

Related Items (12)

Asymptotics for a singularly perturbed GUE, Painlevé III, double-confluent Heun equations, and small eigenvalues ⋮ Truncated Hermite polynomials ⋮ The Jacobi-type polynomials and general Heun equations ⋮ Painlevé V and confluent Heun equations associated with a perturbed Gaussian unitary ensemble ⋮ A singular linear statistic for a perturbed LUE and the Hankel matrices ⋮ Painlevé IV, Chazy II, and asymptotics for recurrence coefficients of semi‐classical Laguerre polynomials and their Hankel determinants ⋮ About families of orthogonal polynomials satisfying Heun's differential equation ⋮ Painlevé IV and the semi-classical Laguerre unitary ensembles with one jump discontinuities ⋮ Matrix integral solutions to the discrete and coupled Leznov lattice equations ⋮ Painlevé IV, σ-form, and the deformed Hermite unitary ensembles ⋮ Differential and difference equations for recurrence coefficients of orthogonal polynomials with hypergeometric weights and Bäcklund transformations of the sixth Painlevé equation ⋮ A note on the asymptotics of the Hankel determinant associated with time-dependent Jacobi polynomials

Uses Software

• DLMF

Cites Work

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• Continuous and discrete Painlevé equations arising from the gap probability distribution of the finite \(n\) Gaussian unitary ensembles
• Painlevé V and a Pollaczek-Jacobi type orthogonal polynomials
• The largest eigenvalue distribution of the Laguerre unitary ensemble
• Heun functions and some of their applications in physics
• Properties of generalized Freud polynomials
• Asymptotic gap probability distributions of the Gaussian unitary ensembles and Jacobi unitary ensembles
• The Riemann--Hilbert approach to strong asymptotics for orthogonal polynomials on [-1,1]
• Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials
• Painlevé III and a singular linear statistics in Hermitian random matrix ensembles. I.
• Asymptotics of determinants of Hankel matrices via non-linear difference equations
• Elliptic orthogonal polynomials
• Perturbed Laguerre unitary ensembles, Hankel determinants, and information theory
• Perturbed Hankel determinant, correlation functions and Painlevé equations
• HEUN FUNCTIONS AND THEIR USES IN PHYSICS
• Painlevé V and the distribution function of a discontinuous linear statistic in the Laguerre unitary ensembles
• Strong and Weak Convergence of Orthogonal Polynomials
• On the linear statistics of Hermitian random matrices
• Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics
• Hypergeometric Expansions of Heun Polynomials
• Die Lösung der linearen Differentialgleichung 2. Ordnung um zwei einfache Singularitäten durch Reihen nach hypergeometrischen Funktionen.
• Unification of one-dimensional Fokker-Planck equations beyond hypergeometrics: Factorizer solution method and eigenvalue schemes
• Avoided crossings of the quartic oscillator
• Thermodynamic relations of the Hermitian matrix ensembles
• Ladder operators and differential equations for orthogonal polynomials
• On the cubic lattice Green functions
• Finite lattice Bethe ansatz systems and the Heun equation
• Center of mass distribution of the Jacobi unitary ensembles: Painlevé V, asymptotic expansions
• Gap Probability Distribution of the Jacobi Unitary Ensemble: An Elementary Treatment, from Finite n to Double Scaling
• Jacobi polynomials from compatibility conditions
• The eigenvalue equation on the Eguchi–Hanson space
• Heun's equation with nearby singularities
• On properties of a deformed Freud weight
• Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions
• Singular linear statistics of the Laguerre unitary ensemble and Painlevé. III. Double scaling analysis
• Coulumb Fluid, Painlevé Transcendents, and the Information Theory of MIMO Systems
• On the simple cubic lattice Green function
• Perturbed Hankel determinants
• CERTAIN EXPANSIONS OF SOLUTIONS OF THE HEUN EQUATION
• INTEGRAL EQUATIONS FOR HEUN FUNCTIONS
• Painlevé V and time-dependent Jacobi polynomials
• Finite temperature expectation values of local fields in the sinh-Gordon model
• The Fuchsian equation of second order with four singularities

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