Approximation of quadratic irrationals and their pierce expansions

Jaume Paradís (), Lluís Bibiloni and Pelegrí Viader ()
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Pelegrí Viader: https://www.upf.edu/web/econ/faculty/-/asset_publisher/6aWmmXf28uXT/persona/id/3418630

Economics Working Papers from Department of Economics and Business, Universitat Pompeu Fabra

Abstract: In this article two aims are pursued: on the one hand, to present a rapidly converging algorithm for the approximation of square roots; on the other hand and based on the previous algorithm, to find the Pierce expansions of a certain class of quadratic irrationals as an alternative way to the method presented in 1984 by J.O. Shallit; we extend the method to find also the Pierce expansions of quadratic irrationals of the form $2 (p-1) (p - \sqrt{p^2 - 1})$ which are not covered in Shallit's work.

Keywords: Quadratic irrationals; Pierce series (search for similar items in EconPapers)
JEL-codes: C00 (search for similar items in EconPapers)
Date: 1996-06
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Persistent link: https://EconPapers.repec.org/RePEc:upf:upfgen:171

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