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arXiv · 1903.09228

Bernoulli and Euler numbers from divergent series

Sergio A. Carrillo
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Abstract

The aim of this note is to provide a simple proof of some well-known identities and recurrences relating classical Bernoulli and Euler numbers by using the Abel sum of the divergent series $\sum_{n=0}^\infty (-1)^{n} (n+1)^k$, $k$ a positive integers. Special attention is placed on the fact that the numerical value of these sums is determined by the linearity of the summation method involved.

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Sergio A. Carrillo. 2019-03-21. Bernoulli and Euler numbers from divergent series. https://arxiv.org/abs/1903.09228

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