Evaluation of Infinite Series by Integrals

Chunli Li and Wenchang Chu
Additional contact information
Chunli Li: School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China
Wenchang Chu: Department of Mathematics and Physics, University of Salento, 73100 Lecce, Italy

Mathematics, 2022, vol. 10, issue 14, 1-14

Abstract: We examine a large class of infinite triple series and establish a general summation formula. This is done by expressing the triple series in terms of definite integrals involving arctangent function that are evaluated in turn in closed forms. Numerous explicit formulae are tabulated for the triple series whose values result in elegant expressions as π , ln 2 and the Catalan constant G .

Keywords: infinite series; Catalan’s constant; integration by parts (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/14/2444/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/14/2444/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:14:p:2444-:d:861931

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().