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Continued fractions for some transcendental numbers

Hone, Andrew N.W. (2015) Continued fractions for some transcendental numbers. Monatshefte fur Mathematik, . ISSN 0026-9255. E-ISSN 1436-5081. (doi:10.1007/s00605-015-0844-2) (KAR id:50921)

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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 non-autonomous recurrence of second order, which entails that $x_n|x_{n+1}$ 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/s00605-015-0844-2
Projects: [UNSPECIFIED] Cluster algebras with periodicity and discrete dynamics over finite fields
Uncontrolled keywords: continued fraction; non-autonomous 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
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)
Hone, Andrew N.W.: https://orcid.org/0000-0001-9780-7369
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