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arXiv · 0909.3184

Large Degree Asymptotics of Generalized Bernoulli and Euler Polynomials

Jose Luis Lopez·Nico M. Temme
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Abstract

Asymptotic expansions are given for large values of $n$ of the generalized Bernoulli polynomials $B_n^μ(z)$ and Euler polynomials $E_n^μ(z)$. In a previous paper López and Temme (1999) these polynomials have been considered for large values of $μ$, with $n$ fixed. In the literature no complete description of the large $n$ asymptotics of the considered polynomials is available. We give the general expansions, summarize known results of special cases and give more details about these results. We use two-point Taylor expansions for obtaining new type of expansions. The analysis is based on contour integrals that follow from the generating functions of the polynomials.

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BibTeXRIS

Jose Luis Lopez, Nico M. Temme. 2009-09-17. Large Degree Asymptotics of Generalized Bernoulli and Euler Polynomials. https://doi.org/10.1016/j.jmaa.2009.08.034

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