Smallest zeros of some types of orthogonal polynomials: asymptotics

作者:

Highlights:

摘要

We establish Mehler–Heine-type formulas for orthogonal polynomials related to rational modifications of Hermite weight on the real line and for Hermite–Sobolev orthogonal polynomials. These formulas give us the asymptotic behaviour of the smallest zeros of the corresponding orthogonal polynomials. Furthermore, we solve a conjecture posed in a previous paper about the asymptotics of the smallest zeros of the Hermite–Sobolev polynomials as well as an open problem concerning the asymptotics of these Sobolev orthogonal polynomials.

论文关键词:primary 42C05,secondary 33C45,Mehler–Heine-type formulas,Sobolev orthogonal polynomials,Asymptotics

论文评审过程:Received 26 November 2003, Available online 13 November 2004.

论文官网地址:https://doi.org/10.1016/j.cam.2004.09.045

Back to Top