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

espanolEn este articulo estudiamos algunas propiedades asintoticas de la sucesion de polinomios monicos ortogonales con respecto a la medida dµ = x 2+a x2+b e −x 2 dx, donde a, b > 0 y a 6= b. En este sentido, estudiamos la asintotica relativa exterior con respecto a los polinomios clasicos de Hermite, ademas son analizadas formulas tipo Mehler-Heine. EnglishIn 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.