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.
%0 Generic
%1 citeulike:3036277
%A Euler, Leonhard
%D 2005
%K Vor1850 available-in-tex-format mathematics number-theory pre1850
%T A commentary on the continued fraction by which the illustrious La Grange has expressed the binomial powers
%U http://arxiv.org/abs/math/0507459
%X 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.
@misc{citeulike:3036277,
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.},
added-at = {2009-08-02T17:14:35.000+0200},
archiveprefix = {arXiv},
author = {Euler, Leonhard},
biburl = {https://www.bibsonomy.org/bibtex/2245152d3746b83d8e93c6b1ca06a036f/rwst},
citeulike-article-id = {3036277},
citeulike-linkout-0 = {http://arxiv.org/abs/math/0507459},
citeulike-linkout-1 = {http://arxiv.org/pdf/math/0507459},
description = {my bookmarks from citeulike},
eprint = {math/0507459},
interhash = {468f147473b77ce2d541a545b6c6812e},
intrahash = {245152d3746b83d8e93c6b1ca06a036f},
keywords = {Vor1850 available-in-tex-format mathematics number-theory pre1850},
month = Jul,
posted-at = {2008-07-23 08:46:37},
priority = {2},
timestamp = {2009-08-06T10:21:16.000+0200},
title = {A commentary on the continued fraction by which the illustrious La Grange has expressed the binomial powers},
url = {http://arxiv.org/abs/math/0507459},
year = 2005
}