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

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

2005-07-22

arxiv.org/abs/math/0507459v1

Mathematics

History and Overview

7 pages, seems to be first English translation of Latin original ``Commentatio in fractionem continuam, qua illustris La Grang

Scientific paper

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.

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