Revisiting the Formula for the Ramanujan Constant of a Series

• Type: Article in International Scientific Journal
• Date: 2022

Authors

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

Journal

Title: Mathematics

Vol. 252

Final page: 1539

Publisher: MDPI

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 0 Citations

Other information

Authenticus ID: P-00W-GYQ

DOI: 10.3390/math10091539

Abstract (EN): The main contribution of this paper is to propose a closed expression for the Ramanujan constant of alternating series, based on the Euler-Boole summation formula. Such an expression is not present in the literature. We also highlight the only choice for the parameter a in the formula proposed by Hardy for a series of positive terms, so the value obtained as the Ramanujan constant agrees with other summation methods for divergent series. Additionally, we derive the closed-formula for the Ramanujan constant of a series with the parameter chosen, under a natural interpretation of the integral term in the Euler-Maclaurin summation formula. Finally, we present several examples of the Ramanujan constant of divergent series.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 15