Asymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials

  1. Navas, L.M. 1
  2. Ruiz, F.J. 2
  3. Varona, J.L. 3
  1. 1 Universidad de Salamanca
    info

    Universidad de Salamanca

    Salamanca, España

    ROR https://ror.org/02f40zc51

  2. 2 Universidad de Zaragoza
    info

    Universidad de Zaragoza

    Zaragoza, España

    ROR https://ror.org/012a91z28

  3. 3 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

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Revista:
Mathematics of Computation

ISSN: 0025-5718

Any de publicació: 2012

Volum: 81

Número: 279

Pàgines: 1707-1722

Tipus: Article

DOI: 10.1090/S0025-5718-2012-02568-3 SCOPUS: 2-s2.0-84864920824 WoS: WOS:000305099000022 GOOGLE SCHOLAR lock_openAccés obert editor

Altres publicacions en: Mathematics of Computation

Resum

We analyze the asymptotic behavior of the Apostol-Bernoulli polynomials Bn(x; λ) in detail. The starting point is their Fourier series on [0, 1] which, it is shown, remains valid as an asymptotic expansion over compact subsets of the complex plane. This is used to determine explicit estimates on the constants in the approximation, and also to analyze oscillatory phenomena which arise in certain cases. These results are transferred to the Apostol-Euler polynomials En(x; λ) via a simple relation linking them to the Apostol-Bernoulli polynomials. © 2011 American Mathematical Society.