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On the continued fraction expansion of certain Engel series

Hone, Andrew N.W. (2016) On the continued fraction expansion of certain Engel series. Journal of Number Theory, 164 . pp. 269-281. ISSN 0022-314X. (doi:10.1016/j.jnt.2015.12.024) (KAR id:53528)

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Official URL
http://dx.doi.org/10.1016/j.jnt.2015.12.024

Abstract

An Engel series is a sum of the reciprocals of an increasing sequence of positive integers, which is such that each term is divisible by the previous one. Here we consider a particular class of Engel series, for which each term of the sequence is divisible by the square of the preceding one, and find an explicit expression for the continued fraction expansion of the sum of a generic series of this kind. As a special case, this includes certain series whose continued fraction expansion was found by Shallit. A family of examples generated by nonlinear recurrences with the Laurent property is considered in detail, along with some associated transcendental numbers.

Item Type: Article
DOI/Identification number: 10.1016/j.jnt.2015.12.024
Subjects: Q Science > QA Mathematics (inc Computing science) > QA150 Algebra > QA241 Number theory
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Andrew Hone
Date Deposited: 18 Dec 2015 13:08 UTC
Last Modified: 16 Feb 2021 13:32 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/53528 (The current URI for this page, for reference purposes)
Hone, Andrew N.W.: https://orcid.org/0000-0001-9780-7369
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