A commentary on the continued fraction by which the illustrious La Grange has expressed the binomial powers
arXiv:math/0507459
Abstract
Euler 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.
7 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