Painlevé III Asymptotics of Hankel Determinants for a Perturbed Jacobi Weight
Zhao‐Yun Zeng, Shuai‐Xia Xu, Yu‐Qiu Zhao
Source abstract
We study the Hankel determinants associated with the weight urn:x-wiley:00222526:media:sapm12090:sapm12090-math-0001 where , , , is analytic in a domain containing [ − 1, 1] and for . In this paper, based on the Deift–Zhou nonlinear steepest descent analysis, we study the double scaling limit of the Hankel determinants as and . We obtain the asymptotic approximations of the Hankel determinants, evaluated in terms of the Jimbo–Miwa–Okamoto σ‐function for the Painlevé III equation. The asymptotics of the leading coefficients and the recurrence coefficients for the perturbed Jacobi polynomials are also obtained.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.