Asymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials
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1
Universidad de Salamanca
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2
Universidad de Zaragoza
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3
Universidad de La Rioja
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ISSN: 0025-5718
Datum der Publikation: 2012
Ausgabe: 81
Nummer: 279
Seiten: 1707-1722
Art: Artikel
Andere Publikationen in: Mathematics of Computation
Projekte im Zusammenhang
Zusammenfassung
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.