The continued fraction expansion of certain Pierce series

  1. Varona, J.L. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Journal:
Journal of Number Theory

ISSN: 0022-314X

Year of publication: 2017

Volume: 180

Pages: 573-578

Type: Article

DOI: 10.1016/J.JNT.2017.05.005 SCOPUS: 2-s2.0-85024484464 WoS: WOS:000407667800031 GOOGLE SCHOLAR

More publications in: Journal of Number Theory

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Abstract

A Pierce series is an alternating sum of the reciprocals of an increasing sequence of positive integers, each one divisible by the previous one. In this short note we study some Pierce series that arise from certain continued fractions. Moreover, we show that the sums of these Pierce series are transcendental numbers. © 2017 Elsevier Inc.