Work

Semiclassical limit of a non-polynomial q-Askey scheme

Year: 2025

Type: article

Abstract: We prove a semiclassical asymptotic formula for the two elements M and Q lying at the bottom of the recently constructed non-polynomial hyperbolic q -Askey scheme. We also prove that the corresponding exponent is a generating function of the canonical transformation between pairs of Darboux coordinates on the monodromy manifold of the Painlevé I and III 3 equations, respectively. Such pairs of coordinates characterize the asymptotics of the tau function of the corresponding Painlevé equation. We conjecture that the other members of the non-polynomial hyperbolic q -Askey scheme yield generating functions associated to the other Painlevé equations in the semiclassical limit.

Source: Journal of Mathematical Analysis and Applications

DOI: 10.1016/j.jmaa.2025.129474

Authors: Jonatan Lenells, Julien Roussillon

Institutions: KTH Royal Institute of Technology, Aalto University

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Academy of Finland, Vetenskapsrådet