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

• Type: Article in International Scientific Journal
• Date: 2021

Authors

Chagas, JQ (Author) Other; Machado, JAT (Author) Other; António Mendes Lopes (Author) FEUP

Journal

Title: Mathematics

Vol. 5

Final page: 2963

Publisher: MDPI

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 0 Citations

Other information

Authenticus ID: 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 38