Asymptotic behavior of the partial derivatives of Laguerre kernels and some applications

Abstract

The aim of this paper is to present some new results about the asymptotic behavior of the partial derivatives of the kernel polynomials associated with the Gamma distribution. We also show how these results can be used in order to obtain the inner relative asymptotics for certain Laguerre-Sobolev type polynomials.The work of the first author (FM) has been supported by Dirección General de Investigación Científica y Técnica, Ministerio de Economía y Competitividad of Spain, grant MTM 2012-36732-C03-01. The work of the second author (MFPV) has been supported by the Research Fellowship Program, Ministerio de Ciencia e Innovación (MTM 2009-12740-C03-01) and Dirección General de Investigación Científica y Técnica, Ministerio de Economía y Competitividad of Spain, grant MTM 2012-36732-C03-01. The work of the third author (YQ) has been partially supported by Dirección General de Investigación Científica y Técnica, Ministerio de Economía y Competitividad of Spain, grant MTM 2012-36732-C03-01