On some asymptotic properties of classical Hermite polynomials modified by a rational factor

Abstract

In this paper we study some asymptotic properties of the sequence of monic polynomials orthogonal with respect to the measure dµ = x 2+a x2+b e −x 2 dx, where a, b > 0 and a 6= b. In this way we study the outer relative asymptotic with respect to the classical Hermite polynomials; besides, Mehler-Heine type formulas are analyzed.

Keywords

• Asymptotics properties
• perturbed Hermite polynomials
• Christoffel and Geronimus perturbations.