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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the irrationality of a certain $q$ series


Authors: Peter B. Borwein and Ping Zhou
Journal: Proc. Amer. Math. Soc. 127 (1999), 1605-1613
MSC (1991): Primary 11J72
Published electronically: February 17, 1999
Erratum: Proc. Amer. Math. Soc. 132 (2004), 3131-3131.
MathSciNet review: 1485462
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that if $q$ is an integer greater than one, $r$ and $s$ are any positive rationals such that $1+q^mr-q^{2m}s\neq 0$ for all integers $m\geq 0$, then

\begin{displaymath}\sum _{j=0}^\infty \frac 1{1+q^jr-q^{2j}s} \end{displaymath}

is irrational and is not a Liouville number.


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Additional Information

Peter B. Borwein
Affiliation: Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
Email: pborwein@cecm.sfu.ca

Ping Zhou
Affiliation: Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
Email: pzhou@cecm.sfu.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04722-X
PII: S 0002-9939(99)04722-X
Received by editor(s): September 16, 1997
Published electronically: February 17, 1999
Communicated by: David E. Rohrlich
Article copyright: © Copyright 1999 by the authors