The origins of Euler's early work on continued fractions

Cretney, Rosanna (2014). The origins of Euler's early work on continued fractions. Historia Mathematica, 41(2) pp. 139–156.

DOI: https://doi.org/10.1016/j.hm.2013.12.004

Abstract

In this paper, I examine Eulerʼs early work on the elementary properties of continued fractions in the 1730s, and investigate its possible links to previous writings on continued fractions by authors such as William Brouncker. By analysing the content of Eulerʼs first paper on continued fractions, ‘De fractionibus continuis dissertatio’ (1737, published 1744) I conclude that, contrary to what one might expect, Eulerʼs work on continued fractions initially arose not from earlier writings on continued fractions, but from a wish to solve the Riccati differential equation.

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