Observations on continued fractions
History and Overview
2018-08-22 v1 Number Theory
Abstract
This is a translation of Euler's Latin paper "De fractionibus continuis observationes" into English. In this paper Euler describes his theory of continued fractions. He teaches, how to transform series into continued fractions, solves the Riccati-Differential equation by means of continued fractions and finds many other interesting formulas and results (e.g, the continued fraction for the quotient of two hypergeometric series usually attributed to Gau{\ss})
Cite
@article{arxiv.1808.07006,
title = {Observations on continued fractions},
author = {Leonhard Euler and Alexander Aycock},
journal= {arXiv preprint arXiv:1808.07006},
year = {2018}
}
Comments
66 pages; other translations can also be found at http://eulerarchive.maa.org/ and https://www.agtz.mathematik.uni-mainz.de/algebraische-geometrie/van-straten/euler-kreis-mainz/ at the Euler-Kreis Mainz