The Jacobi-type polynomials and general Heun equations

DOI10.1016/j.aml.2023.108694zbMath1525.33009OpenAlexW4366483032MaRDI QIDQ6112131

Mengkun Zhu, Yang Chen, Dan Wang

Publication date: 7 July 2023

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2023.108694

zbMATH Keywords

asymptoticsorthogonal polynomialsgeneral Heun equation

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Explicit solutions, first integrals of ordinary differential equations (34A05) Asymptotic representations in the complex plane (30E15)

Cites Work

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• Painlevé V and the Hankel determinant for a singularly perturbed Jacobi weight
• The Riemann--Hilbert approach to strong asymptotics for orthogonal polynomials on [-1,1]
• Semi-classical Jacobi polynomials, Hankel determinants and asymptotics
• Painlevé V for a Jacobi unitary ensemble with random singularities
• 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
• Evenness symmetry and inter-relationships between gap probabilities in random matrix theory
• Painlevé III Asymptotics of Hankel Determinants for a Perturbed Jacobi Weight
• Gap probabilities for edge intervals in finite Gaussian and Jacobi unitary matrix ensembles
• Jacobi polynomials from compatibility conditions
• Differential, difference, and asymptotic relations for Pollaczek–Jacobi type orthogonal polynomials and their Hankel determinants
• Orthogonal polynomials, asymptotics, and Heun equations
• Painlevé V and time-dependent Jacobi polynomials

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