Hone, Andrew N.W. (2016) On the continued fraction expansion of certain Engel series. Journal of Number Theory, 164 . pp. 269281. ISSN 0022314X. (doi:10.1016/j.jnt.2015.12.024) (KAR id:53528)
PDF
Language: English 

Download (232kB)
Preview

Preview 
This file may not be suitable for users of assistive technology.
Request an accessible format


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/0000000197807369 
 Link to SensusAccess
 Export to:
 RefWorks
 EPrints3 XML
 BibTeX
 CSV
 Depositors only (login required):