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

    Universidad de Salamanca

    Salamanca, España


  2. 2 Universidad de Zaragoza

    Universidad de Zaragoza

    Zaragoza, España


  3. 3 Universidad de La Rioja

    Universidad de La Rioja

    Logroño, España


Mathematics of Computation

ISSN: 0025-5718

Year of publication: 2012

Volume: 81

Issue: 279

Pages: 1707-1722

Type: Article

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

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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.