# 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 10.1007/s00605-015-0844-2 [UNSPECIFIED] Cluster algebras with periodicity and discrete dynamics over finite fields continued fraction; non-autonomous recurrence; transcendental number Q Science > QA Mathematics (inc Computing science) > QA150 Algebra > QA241 Number theory Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science Andrew Hone 13 Oct 2015 20:20 UTC 16 Feb 2021 13:28 UTC https://kar.kent.ac.uk/id/eprint/50921 (The current URI for this page, for reference purposes) https://orcid.org/0000-0001-9780-7369