Overview in Summabilities: Summation Methods for Divergent Series, Ramanujan Summation and Fractional Finite Sums

• Tipo: Artigo em Revista Científica Internacional
• Data: 2021

Autores

Chagas, JQ (Autor) Outra; Machado, JAT (Autor) Outra; António Mendes Lopes (Autor) FEUP

Revista

Título: Mathematics

Vol. 5

Página Final: 2963

Editora: MDPI

Indexação

ISI Web of Knowledge - 0 Citações

Scopus - 0 Citações

Outras Informações

ID Authenticus: P-00V-Q59

DOI: 10.3390/math9222963

Abstract (EN): This work presents an overview of the summability of divergent series and fractional finite sums, including their connections. Several summation methods listed, including the smoothed sum, permit obtaining an algebraic constant related to a divergent series. The first goal is to revisit the discussion about the existence of an algebraic constant related to a divergent series, which does not contradict the divergence of the series in the classical sense. The well-known Euler-Maclaurin summation formula is presented as an important tool. Throughout a systematic discussion, we seek to promote the Ramanujan summation method for divergent series and the methods recently developed for fractional finite sums.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 38