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Asymptotic Approximations between the Hahn-Type Polynomials and Hermite, Laguerre and Charlier Polynomials

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Abstract

It has been shown in Ferreira et al. (Adv. Appl. Math 31:61–85, [2003]), López and Temme (Methods Appl. Anal. 6:131–196, [1999]; J. Cpmput. Appl. Math. 133:623–633, [2001]) that the three lower levels of the Askey table of hypergeometric orthogonal polynomials are connected by means of asymptotic expansions. In this paper we continue with that investigation and establish asymptotic connections between the fourth level and the two lower levels: we derive twelve asymptotic expansions of the Hahn, dual Hahn, continuous Hahn and continuous dual Hahn polynomials in terms of Hermite, Charlier and Laguerre polynomials. From these expansions, several limits between polynomials are derived. Some numerical experiments give an idea about the accuracy of the approximations and, in particular, about the accuracy in the approximation of the zeros of the Hahn, dual Hahn, continuous Hahn and continuous dual Hahn polynomials in terms of the zeros of the Hermite, Charlier and Laguerre polynomials.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada IUMAZ, Universidad de Zaragoza, Zaragoza, Spain

    Chelo Ferreira

  2. Departamento de Ingeniería Matemática e Informática, Universidad Pública de Navarra, Pamplona, Spain

    José L. López & Pedro J. Pagola

Authors
  1. Chelo Ferreira
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  2. José L. López
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  3. Pedro J. Pagola
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Correspondence to José L. López.

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Ferreira, C., López, J.L. & Pagola, P.J. Asymptotic Approximations between the Hahn-Type Polynomials and Hermite, Laguerre and Charlier Polynomials. Acta Appl Math 103, 235–252 (2008). https://doi.org/10.1007/s10440-008-9233-3

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  • DOI: https://doi.org/10.1007/s10440-008-9233-3

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