Observations on continued fractions

2018/08/10 by Euler, Leonhard, Aycock, Alexander
#FOS: Mathematics #History and Overview (math.HO) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1808.07006

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 Gauß)

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