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On the irrationality of a certain series

Authors:	Peter B Borwein Ping Zhou

Institution:	Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6 ; Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6

Abstract:	We prove that if is an integer greater than one, and 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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