Orthogonal Polynomials for the Gaussian Weight with a Jump and Discrete Painlev\'e Equations
Exactly Solvable and Integrable Systems
2025-08-22 v1 Mathematical Physics
Classical Analysis and ODEs
math.MP
Abstract
We describe a refined version of the discrete Painlev\'e identification problem that emphasizes the importance on going beyond just the surface type in describing a discrete Painlev\'e dynamic. We give an example of solving such identification problem for a particular recurrence relation that previously appeared in studying orthogonal polynomials for the Gaussian weight with a single jump.
Keywords
Cite
@article{arxiv.2508.12202,
title = {Orthogonal Polynomials for the Gaussian Weight with a Jump and Discrete Painlev\'e Equations},
author = {Anton Dzhamay and Elizaveta Trunina},
journal= {arXiv preprint arXiv:2508.12202},
year = {2025}
}
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13 pages