Asymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials (Q2894530)
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scientific article; zbMATH DE number 6051357
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Asymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials |
scientific article; zbMATH DE number 6051357 |
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Asymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials (English)
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29 June 2012
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Apostol-Bernoulli polynomials
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Apostol-Euler polynomials
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Fourier series
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asymptotic estimates
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The authors reveal a simple relation linking the two classes of polynomials in the title, and, therefore, they treat in detail only those associated with Bernoulli. A Fourier series developed in an earlier paper by the same authors [J. Approx. Theory 163, No. 1, 22--40 (2011; Zbl 1253.11028)] is shown to remain valid as an asymptotic expansion over compact subsets of the complex plane. This, in turn, is used to deduce explicit asymptotic estimates for the polynomials in question.
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