%0 Generic %1 citeulike:3036249 %A Euler, Leonhard %D 2007 %K Vor1800 available-in-tex-format combinatorics mathematics pre1800 %T General observations on series whose terms proceed as the sines and cosines of multiples of angles %U http://arxiv.org/abs/0709.0557 %X Translated from the Latin original, Öbservationes 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=\phi+i\sin\phi\$. He does \$n=\$ positive and negative integers, and \$n=1/2, -1/2\$, and particular values of \$\phi\$.

@misc{citeulike:3036249, 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 \phi+i\sin\phi\$. He does \$n=\$ positive and negative integers, and \$n={1/2}, -{1/2}\$, and particular values of \$\phi\$.}, added-at = {2009-08-02T17:14:35.000+0200}, archiveprefix = {arXiv}, author = {Euler, Leonhard}, biburl = {https://www.bibsonomy.org/bibtex/23c170c107e5529e4fc1197edf36b8418/rwst}, citeulike-article-id = {3036249}, citeulike-linkout-0 = {http://arxiv.org/abs/0709.0557}, citeulike-linkout-1 = {http://arxiv.org/pdf/0709.0557}, description = {my bookmarks from citeulike}, eprint = {0709.0557}, interhash = {5db6dcb49a8c0966278934ba782c85e8}, intrahash = {3c170c107e5529e4fc1197edf36b8418}, keywords = {Vor1800 available-in-tex-format combinatorics mathematics pre1800}, month = Sep, posted-at = {2008-07-23 08:36:17}, priority = {2}, timestamp = {2009-08-05T17:09:01.000+0200}, title = {General observations on series whose terms proceed as the sines and cosines of multiples of angles}, url = {http://arxiv.org/abs/0709.0557}, year = 2007 }