Affiliations: Departamento de Matemáticas and IUMA, Univ. de Zaragoza, Zaragoza, Spain | Departamento de Estadística y Matemática Aplicada, Instituto Carlos I de Física Teórica y Computacional, Univ. de Almería, Almería, Spain
Note: [] Corresponding author: Ana Peña, Departamento de Matemáticas, Universidad de Zaragoza, 50009-Zaragoza, Spain. Tel.: +34 976761328; Fax: +34 976761338; E-mail: [email protected].
Abstract: We consider a generalization of the classical Hermite polynomials by the addition of terms involving derivatives in the inner product. This type of generalization has been studied in the literature from the point of view of the algebraic properties. Thus, our aim is to study the asymptotics of this sequence of nonstandard orthogonal polynomials. In fact, we obtain Mehler–Heine type formulas for these polynomials and, as a consequence, we prove that there exists an acceleration of the convergence of the smallest positive zeros of these generalized Hermite polynomials towards the origin.
Keywords: asymptotics, Hermite polynomials, Mehler–Heine type formulas, zeros, Bessel functions
