English

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 nn 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}
}