Asymptotic Approximations between the Hahn-Type Polynomials and Hermite, Laguerre and Charlier Polynomials |
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Authors: | Chelo Ferreira José L López Pedro J Pagola |
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Institution: | (1) Departamento de Matemática Aplicada IUMAZ, Universidad de Zaragoza, Zaragoza, Spain;(2) Departamento de Ingeniería Matemática e Informática, Universidad Pública de Navarra, Pamplona, Spain |
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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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Keywords: | Hahn dual Hahn continuous Hahn continuous dual Hahn Laguerre Charlier Hermite polynomials Askey scheme of hypergeometric orthogonal polynomials Asymptotic expansions Limits between orthogonal polynomials |
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