A commentary on the continued fraction by which the illustrious La Grange has expressed the binomial powers

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dc.creatorEuler, Leonhard
dc.date2005-07-22
dc.date.accessioned2026-07-07T05:21:54Z
dc.date.available2026-07-07T05:21:54Z
dc.descriptionEuler gives a continued fraction representation of (1+x)^n involving 1,3,5,7,... and n^2-1,n^2-4,n^3-9,... and squares of z, for x=2y and y=z/(1-z). He evaluates this continued fraction at z=t sqrt(-1), for ``vanishing'' n, and for infinite n.
dc.description7 pages, seems to be first English translation of Latin original ``Commentatio in fractionem continuam, qua illustris La Grange potestates binomiales expressit'', Memoires de l'academie des sciences de St.-Petersbourg 6 (1818), 3-11, E750
dc.identifierhttps://arxiv.org/abs/math/0507459
dc.identifierhttp://arxiv.org/abs/math/0507459
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75863
dc.subjectHistory and Overview
dc.subjectNumber Theory
dc.subject01A50; 11A55
dc.titleA commentary on the continued fraction by which the illustrious La Grange has expressed the binomial powers
dc.typetext

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