Relation of the cyclotomic equation with the harmonic and derived series
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:

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): Física Teórica (Departamento de Física Teórica)

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