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On the real roots of Euler polynomials

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Abstract

We show how are located the positive roots of the Euler polynomiale n of degreen. We give an upper bound and a lower bound for the greatest root. This permits to determine an integerv (n) such that the number of positive roots ofE n is eitherv (n) orv (n) +2. We also study the behaviour of ther-th positive root ofE n asn tends to infinity.

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  1. Centre d'Orsay, Université de Paris-Sud, 91405, Orsay, Cedex, France

    Hubert Delange

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  1. Hubert Delange
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Delange, H. On the real roots of Euler polynomials. Monatshefte für Mathematik 106, 115–138 (1988). https://doi.org/10.1007/BF01298833

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  • DOI: https://doi.org/10.1007/BF01298833

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