Relation of the cyclotomic equation with the harmonic and derived series

Boya, L.J. (Universidad de Zaragoza) ; Rivera, C.

Resumen: We 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.

Idioma: Inglés

DOI: 10.1155/2015/950521

Año: 2015

Publicado en: The Scientific World Journal 2015 (2015), 950521 [7 pp.]
ISSN: 2356-6140

Factor impacto SCIMAGO: 0.381 - Environmental Science (miscellaneous) (Q2) - Medicine (miscellaneous) (Q3) - Biochemistry, Genetics and Molecular Biology (miscellaneous) (Q3)

Financiación: info:eu-repo/grantAgreement/ES/CICYT/FPA2006-02315
Financiación: info:eu-repo/grantAgreement/ES/DGA/2007-E242

Tipo y forma: Article (Published version)

Área (Departamento): Área Física Teórica (Dpto. Física Teórica)