English

Bernoulli and Euler numbers from divergent series

Classical Analysis and ODEs 2019-03-25 v1

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 n=0(1)n(n+1)k\sum_{n=0}^\infty (-1)^{n} (n+1)^k, kk 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.

Keywords

Cite

@article{arxiv.1903.09228,
  title  = {Bernoulli and Euler numbers from divergent series},
  author = {Sergio A. Carrillo},
  journal= {arXiv preprint arXiv:1903.09228},
  year   = {2019}
}
R2 v1 2026-06-23T08:15:36.589Z