Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

On the irrationality of a certain series

Author(s): Peter B. Borwein; Ping Zhou
Journal: Proc. Amer. Math. Soc. 127 (1999), 1605-1613.
MSC (1991): Primary 11J72
Posted: February 17, 1999
Errata: 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 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.

References:

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