Asymptotics for a generalization of Hermite polynomials

Details Asymptotics for a generalization of Hermite polynomials Asymptotics for a generalization of Hermite polynomials

2009-09-03

arxiv.org/abs/0909.0617v1

Mathematics

Classical Analysis and ODEs

18 pages

Scientific paper

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.

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