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Bounds for the zeros of symmetric Kravchuk polynomials

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Abstract

Sharp bounds for the zeros of symmetric Kravchuk polynomials K n (x;M) are obtained. The results provide a precise quantitative meaning of the fact that Kravchuk polynomials converge uniformly to Hermite polynomials, as M tends to infinity. They show also how close the corresponding zeros of two polynomials from these sequences of classical orthogonal polynomials are.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada II, E.E. Telecomunicación, Universidade de Vigo, Campus Lagoas-Marcosende, 36310, Vigo, Spain

    Iván Area

  2. Departamento de Matemática Aplicada, IBILCE, Universidade Estadual Paulista, 15054-000, São José do Rio Preto, SP, Brazil

    Dimitar K. Dimitrov

  3. Departamento de Matemática Aplicada II, E.E. Industrial, Universidade de Vigo, Campus Lagoas-Marcosende, 36310, Vigo, Spain

    Eduardo Godoy

  4. Departamento de Ciência e Tecnologia, Universidade Federal de São Paulo, 12231-280, São José dos Campos, SP, Brazil

    Vanessa Paschoa

Authors
  1. Iván Area
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  2. Dimitar K. Dimitrov
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  3. Eduardo Godoy
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  4. Vanessa Paschoa
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Corresponding author

Correspondence to Iván Area.

Additional information

Research supported by the Brazilian foundations FAPESP under Grants 2009/13832–9 and 2013/23606–1, and CNPq under Grant 307183/2013–0, and by the Ministerio de Ministerio de Economía y Competitividad of Spain under grant MTM2012–38794–C02–01, co-financed by the European Community fund FEDER. The first author thanks the Departamento de Matemática Aplicada, IBILCE, Universidade Estadual Paulista, where the research on the paper was performed during his visit supported by FAPESP.

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Area, I., Dimitrov, D.K., Godoy, E. et al. Bounds for the zeros of symmetric Kravchuk polynomials. Numer Algor 69, 611–624 (2015). https://doi.org/10.1007/s11075-014-9916-y

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  • DOI: https://doi.org/10.1007/s11075-014-9916-y

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