General observations on series whose terms proceed as the sines and cosines of multiples of angles

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dc.creatorEuler, Leonhard
dc.date2007-09-05
dc.date.accessioned2026-07-07T08:27:43Z
dc.date.available2026-07-07T08:27:43Z
dc.descriptionTranslated from the Latin original, "Observationes generales circa series, quarum termini secundum sinus vel cosinus angulorum multiplorum progrediuntur" (1777). E655 in the Enestrom index. Euler looks at the binomial expansion $(1+x)^n$ for $x=\cos ϕ+i\sinϕ$. He does $n=$ positive and negative integers, and $n={1/2}, -{1/2}$, and particular values of $ϕ$.
dc.description12 pages. E655
dc.identifierhttps://arxiv.org/abs/0709.0557
dc.identifierhttp://arxiv.org/abs/0709.0557
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/137362
dc.subjectHistory and Overview
dc.subjectClassical Analysis and ODEs
dc.subject01A50
dc.titleGeneral observations on series whose terms proceed as the sines and cosines of multiples of angles
dc.typetext

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