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Bernoulli and Euler numbers from divergent series

2019/03/21 by Sergio A. Carrillo, Carrillo, Sergio A.
Mathematics · #11B68 #40G10 #Advanced Mathematical Identities #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1903.09228

openalex publication_date 2019/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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, 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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