The origins of Euler's early work on continued fractions |
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Authors: | Rosanna Cretney |
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Affiliation: | Department of Mathematics and Statistics, The Open University, Milton Keynes, Buckinghamshire, MK7 6AA, UK |
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Abstract: | In this paper, I examine Euler's 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 Euler's first paper on continued fractions, ‘De fractionibus continuis dissertatio’ (1737, published 1744) I conclude that, contrary to what one might expect, Euler's 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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Keywords: | 01A50 34A03 01A45 26A03 |
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