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, ln2 and the Catalan constant G.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference25 articles.
1. An Introduction to the Theory of Infinite Series;Bromwich,1908
2. Theory and Applications of Infinite Series;Knopp,1928
3. On the evaluation of some multiple series;Mordell;J. Lond. Math. Soc.,1958
4. On some infinite series of L. J. Mordell and their analogues
5. Tornheim-like series, harmonic numbers and zeta values;Aliev;arXiv,2020
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献