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Continued fractions and irrationality exponents for modified engel and pierce series

Hone, Andrew N.W., Varona, Juan Luis (2018) Continued fractions and irrationality exponents for modified engel and pierce series. Monatshefte fur Mathematik, . pp. 1-16. ISSN 0026-9255. E-ISSN 1436-5081. (doi:10.1007/s00605-018-1244-1)

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Official URL
https://doi.org/10.1007/s00605-018-1244-1

Abstract

An Engel series is a sum of reciprocals of a non-decreasing

by the previous one, and a Pierce series is an alternating sum of the

number, we show that there is a family of Engel series which when

expansion is determined explicitly by the corresponding sequence

second order. We also present an analogous result for a rational number

rational number combined with either an Engel or a Pierce series), the

identify infinite families of transcendental numbers ? whose irrationality

continued fraction expansion for an arbitrary rational number added to

j.

Item Type: Article
DOI/Identification number: 10.1007/s00605-018-1244-1
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Andrew N W Hone
Date Deposited: 20 Nov 2018 11:03 UTC
Last Modified: 01 Dec 2019 00:00 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/70203 (The current URI for this page, for reference purposes)
Hone, Andrew N.W.: https://orcid.org/0000-0001-9780-7369
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