Smallest zeros of some types of orthogonal polynomials: asymptotics

Authors:
Juan José Moreno-Balcázar
Affiliations:
Departamento de Estadística y Matemática Aplicada, Universidad de Almería, Almería, Spain and Instituto de Física Teórica y Computacional, Universidad de Granada, Gra ...
Venue:
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the conference on orthogonal functions and related topics held in honor of Olav Njåstad
Year:
2005

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Abstract

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.