000056084 001__ 56084 000056084 005__ 20210121114443.0 000056084 0247_ $$2doi$$a10.1155/2015/950521 000056084 0248_ $$2sideral$$a89567 000056084 037__ $$aART-2015-89567 000056084 041__ $$aeng 000056084 100__ $$0(orcid)0000-0002-9065-7369$$aBoya, L.J.$$uUniversidad de Zaragoza 000056084 245__ $$aRelation of the cyclotomic equation with the harmonic and derived series 000056084 260__ $$c2015 000056084 5060_ $$aAccess copy available to the general public$$fUnrestricted 000056084 5203_ $$aWe associate some (old) convergent series related to definite integrals with the cyclotomic equation ¿¿ - 1 = 0, for several natural numbers m for example, for ¿=3,¿3 -1=(¿-1)(1+¿+¿2) leads to ¿1¿¿(1/(1+¿+¿2))=¿/(3v3)=(1-1/2)+(1/4 - 1/5) + (1/7 - 1/8) + · · · . 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. 000056084 536__ $$9info:eu-repo/grantAgreement/ES/CICYT/FPA2006-02315$$9info:eu-repo/grantAgreement/ES/DGA/2007-E242 000056084 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000056084 592__ $$a0.381$$b2015 000056084 593__ $$aEnvironmental Science (miscellaneous)$$c2015$$dQ2 000056084 593__ $$aMedicine (miscellaneous)$$c2015$$dQ3 000056084 593__ $$aBiochemistry, Genetics and Molecular Biology (miscellaneous)$$c2015$$dQ3 000056084 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000056084 700__ $$aRivera, C. 000056084 7102_ $$12004$$2405$$aUniversidad de Zaragoza$$bDpto. Física Teórica$$cÁrea Física Teórica 000056084 773__ $$g2015 (2015), 950521 [7 pp.]$$pSci. world j.$$tThe Scientific World Journal$$x2356-6140 000056084 8564_ $$s1962012$$uhttps://zaguan.unizar.es/record/56084/files/texto_completo.pdf$$yVersión publicada 000056084 8564_ $$s64571$$uhttps://zaguan.unizar.es/record/56084/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000056084 909CO $$ooai:zaguan.unizar.es:56084$$particulos$$pdriver 000056084 951__ $$a2021-01-21-10:41:29 000056084 980__ $$aARTICLE