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

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

2007-09-05

arxiv.org/abs/0709.0557v1

Mathematics

History and Overview

12 pages. E655

Scientific paper

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 $x=\cos \phi+i\sin\phi$. He does $n=$ positive and negative
integers, and $n={1/2}, -{1/2}$, and particular values of $\phi$.

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