J. Aust. Math. Soc.
77 (2004), 305-319
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The unreasonable effectualness of continued function expansions
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Greg Martin
Department of Mathematics
University of British Columbia
Room 121, 1984 Mathematics Road
Vancouver, BC V6T 1Z2
Canada
gerg@math.ubc.ca
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Abstract
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Many generalizations of continued fractions,
where the reciprocal function has been replaced
by a more general function, have been studied,
and it is often asked whether such generalized
expansions can have nice properties. For
instance, we might ask that algebraic numbers of
a given degree have periodic expansions, just as
quadratic irrationals have periodic continued
fractions; or we might ask that familiar
transcendental constants such as
or
have periodic or terminating expansions. In this
paper, we show that there exist such generalized
continued function expansions with essentially
any desired behaviour.
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