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SOME EXACT ALGEBRAIC EXPRESSIONS FOR THE TAILS OF TASOEV CONTINUED FRACTIONS

Part of: Elementary number theory Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  11 October 2012

TAKAO KOMATSU
TAKAO KOMATSU*
Affiliation:
Graduate School of Science and Technology, Hirosaki University, Hirosaki 036-8561, Japan (email: komatsu@cc.hirosaki-u.ac.jp)
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Abstract

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Denote the nth convergent of the continued fraction α=[a0;a1,a2,…] by pn/qn=[a0;a1,…,an]. In this paper we give exact formulae for the quantities Dn:=qnα−pn in several typical types of Tasoev continued fractions. A simple example of the type of Tasoev continued fraction considered is α=[0;ua,ua2,ua3,…].

Keywords

Tasoev continued fractionsHurwitz continued fractionscontinued fractionsDiophantine approximations

MSC classification

Secondary: 11A55: Continued fractions 11J70: Continued fractions and generalizations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 92 , Issue 2 , April 2012 , pp. 179 - 193
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

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