Recurrence coefficients for the time-evolved Jacobi weight and discrete Painlevé equations on the D₅ Sakai surface

2025/11/06 by Mengkun Zhu, Siqi Chen, Zhu, Mengkun +3
Mathematics · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.2511.04176

openalex publication_date 2025/11/06 · openalex created_date 2025/11/08 · openalex updated_date 2026/07/28

Abstract

In this paper, we focus on the relationship between the d-P(A₃⁽¹⁾/D₅⁽¹⁾) equations and a time-evolved Jacobi weight, w(x)=x^α(1-x)^βe^-sx, x∈[0,1], α,β> -1, s>0. From the perspective of Sakai's geometric theory of Painlevé equations, we derive that a recurrence relation closely related to the recurrence coefficients of monic polynomials orthogonal with w(x) is equivalent to the standard d-P(A₃⁽¹⁾/D₅⁽¹⁾) equation.

Citations

• Painlev 'e-type differential equations for the recurrence coefficients\n of semi-classical orthogonal polynomials.

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