J. Aust. Math. Soc.  77 (2004), 305-319
The unreasonable effectualness of continued function expansions

Greg Martin
  Department of Mathematics
  University of British Columbia
  Room 121, 1984 Mathematics Road
  Vancouver, BC V6T 1Z2

Many generalizations of continued fractions, where the reciprocal function has been replaced by a more general function, have been studied, and it is often asked whether such generalized expansions can have nice properties.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 $e$ or $\pi$ 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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