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Approximation of quadratic irrationals and their pierce expansions

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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.

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  • Jaume Paradís & Lluís Bibiloni & Pelegrí Viader, 1996. "Approximation of quadratic irrationals and their pierce expansions," Economics Working Papers 171, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:171
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    Keywords

    Quadratic irrationals; Pierce series;

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General

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