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

2007/09/05 by Leonhard Euler, Euler, Leonhard
Mathematics · #01A50 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #History and Overview (math.HO) #math.CA #math.HO #msc:01A50

paper · pdf · doi:10.48550/arxiv.0709.0557

12 pages. E655

arxiv created 2007/09/05 · arxiv updated 2009/12/01

Abstract

Translated 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+isinϕ. He does n= positive and negative integers, and n=1/2, -1/2, and particular values of ϕ.

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