Relation of the Cyclotomic Equation with the Harmonic and Derived SeriesReport as inadecuate




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The Scientific World Journal - Volume 2015 2015, Article ID 950521, 7 pages -

Research ArticleDepartamento de Física Teórica, Universidad de Zaragoza, 50009 Zaragoza, Spain

Received 21 October 2014; Accepted 13 December 2014

Academic Editor: Abdelalim A. Elsadany

Copyright © 2015 Luis J. Boya and Cristian Rivera. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We associate some old convergent series related to definite integrals with the cyclotomic equation , for several natural numbers m; for example, for , leads to . In some cases, we express the results in terms of the Dirichlet characters. Generalizations for arbitrary m are well defined but do imply integrals and-or series summations rather involved.





Author: Luis J. Boya and Cristian Rivera

Source: https://www.hindawi.com/



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