Irrationality measures for almost periodic continued fractions

We give general results which provide asymptotic irrationality measures and estimations for the denominators of the convergents for certain almost periodic simple continued fraction expansions. As an application we obtain new irrationality measures, for example, to Napier's constant , certain p...

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Bibliographic Details
Published inGeorgian mathematical journal Vol. 23; no. 1; pp. 55 - 67
Main Authors Dodulíková, Silvia, Hančl, Jaroslav, Kolouch, Ondřej, Leinonen, Marko, Leppälä, Kalle
Format Journal Article
LanguageEnglish
Published De Gruyter 01.03.2016
Subjects
11A55
11J82
Continued fraction
measure of irrationality
number
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Summary:We give general results which provide asymptotic irrationality measures and estimations for the denominators of the convergents for certain almost periodic simple continued fraction expansions. As an application we obtain new irrationality measures, for example, to Napier's constant , certain powers of , and a ratio of modified Bessel functions.
ISSN:1072-947X
1572-9176
DOI:10.1515/gmj-2015-0056