Differential and Difference Equations for Recurrence Coefficients of Orthogonal Polynomials with a Singularly Perturbed Laguerre-type Weight
Classical Analysis and ODEs
2023-08-21 v1 Mathematical Physics
math.MP
Abstract
We are concerned with the monic orthogonal polynomials with respect to a singularly perturbed Laguerre-type weight. By using the ladder operator approach, we derive a complicated system of nonlinear second-order difference equations satisfied by the recurrence coefficients. This allows us to derive the large asymptotic expansions of the recurrence coefficients. In addition, we also obtain a system of differential-difference equations for the recurrence coefficients.
Keywords
Cite
@article{arxiv.2209.07128,
title = {Differential and Difference Equations for Recurrence Coefficients of Orthogonal Polynomials with a Singularly Perturbed Laguerre-type Weight},
author = {Chao Min and Yuan Cheng and Yang Chen},
journal= {arXiv preprint arXiv:2209.07128},
year = {2023}
}