Families of Rational Numbers with Predictable Engel Product Expansions
R. S. Melham
Department of Mathematical Sciences
University of Technology, Sydney
PO Box 123, Broadway, NSW 2007
In 1987 Knopfmacher and Knopfmacher published new infinite product
expansions for real numbers 0 < A < 1 and
A > 1. They called these
expansions Engel product expansions. At that time they had
difficulty finding rational 0 < A < 1 for which the Engel product
expansion is predictable. Later, in 1993, Arnold Knopfmacher
presented many such families of rationals. In this paper we add to
Arnold Knopfmacher's list of such families.
Full version: pdf,
Received July 9 2009;
revised version received August 5 2009.
Published in Journal of Integer Sequences, August 30 2009.
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