Commentatio in fractionem continuam, qua illustris La Grange potestates binomiales expressit
History and Overview
2012-02-02 v1
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 and deduces a continued fraction for log, arctan, etc. The paper is translated from Euler's Latin original into German.
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Cite
@article{arxiv.1202.0035,
title = {Commentatio in fractionem continuam, qua illustris La Grange potestates binomiales expressit},
author = {Leonhard Euler and Artur Diener and Alexander Aycock},
journal= {arXiv preprint arXiv:1202.0035},
year = {2012}
}