Orthogonal polynomials, bi-confluent Heun equations and semi-classical weights

DOI10.1080/10236198.2020.1812595zbMath1465.33009OpenAlexW3082492806MaRDI QIDQ5132589

Yang Chen, Dan Wang, Mengkun Zhu

Publication date: 12 November 2020

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10236198.2020.1812595

zbMATH Keywords

orthogonal polynomialsasymptoticsemi-classicalbi-confluent Heun equation

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Asymptotic expansions of solutions to PDEs (35C20) Other special orthogonal polynomials and functions (33C47) Numerical methods for difference and functional equations, recurrence relations (65Q99)

Related Items (4)

Asymptotics for a singularly perturbed GUE, Painlevé III, double-confluent Heun equations, and small eigenvalues ⋮ Painlevé V and confluent Heun equations associated with a perturbed Gaussian unitary ensemble ⋮ Painlevé IV and the semi-classical Laguerre unitary ensembles with one jump discontinuities ⋮ Painlevé IV, σ-form, and the deformed Hermite unitary ensembles

Uses Software

• Mathematica
• DLMF

Cites Work

• Hankel determinant and orthogonal polynomials for a Gaussian weight with a discontinuity at the edge
• The relationship between semiclassical Laguerre polynomials and the fourth Painlevé equation
• Solutions of the bi-confluent Heun equation in terms of the Hermite functions
• The recurrence coefficients of semi-classical Laguerre polynomials and the fourth Painlevé equation
• Hankel determinant and orthogonal polynomials for the Gaussian weight with a jump
• Discrete Painlevé equations for recurrence coefficients of semiclassical Laguerre polynomials
• Ladder operators and differential equations for orthogonal polynomials
• The recurrence coefficients of a semi-classical Laguerre polynomials and the large n asymptotics of the associated Hankel determinant
• Painlevé transcendents and the Hankel determinants generated by a discontinuous Gaussian weight
• Orthogonal polynomials with discontinuous weights
• Jacobi polynomials from compatibility conditions
• On properties of a deformed Freud weight
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