English

The Szeg\"o curve and Laguerre polynomials with large negative parameters

Complex Variables 2010-11-10 v1

Abstract

We study the asymptotic zero distribution of the rescaled Laguerre polynomials, Ln(αn)(nz)\displaystyle L_n^{(\alpha_n)}(nz), with the parameter αn\alpha_n varying in such a way that limnαn/n=1\displaystyle \lim_{n\rightarrow \infty}\alpha_n/n=-1. The connection with the so-called Szeg\"{o} curve will be showed.

Keywords

Cite

@article{arxiv.1011.2017,
  title  = {The Szeg\"o curve and Laguerre polynomials with large negative parameters},
  author = {Carlos Díaz Mendoza and Ramón Orive},
  journal= {arXiv preprint arXiv:1011.2017},
  year   = {2010}
}