Hone, Andrew N.W. (2015) Continued fractions for some transcendental numbers. Monatshefte fur Mathematik, . ISSN 00269255. EISSN 14365081. (doi:10.1007/s0060501508442) (KAR id:50921)
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Official URL: http://link.springer.com/article/10.1007/s0060501... 
Abstract
We consider series of the form $p/q + \sum_{j=2}^\infty 1/x_j$, where $x_1=q$ and the integer sequence $x_n$ satisfies a certain nonautonomous recurrence of second order, which entails that $x_nx_{n+1}$ for n?1. It is shown that the terms of the sequence, and multiples of the ratios of successive terms, appear interlaced in the continued fraction expansion of the sum of the series, which is a transcendental number.
Item Type:  Article 

DOI/Identification number:  10.1007/s0060501508442 
Projects:  Cluster algebras with periodicity and discrete dynamics over finite fields 
Uncontrolled keywords:  continued fraction; nonautonomous recurrence; transcendental number 
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 
Funders:  [UNSPECIFIED] EPSRC 
Depositing User:  Andrew Hone 
Date Deposited:  13 Oct 2015 20:20 UTC 
Last Modified:  16 Feb 2021 13:28 UTC 
Resource URI:  https://kar.kent.ac.uk/id/eprint/50921 (The current URI for this page, for reference purposes) 
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