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CATCF was established in 1992 as a paper journal published once a year to provide an international forum for reporting and discussing developments in the analytic theory of continued fractions and closely related topics. John Gill from University of Southern Colorado (now Colorado State University, Pueblo) in Pueblo, Colorado, USA and John H. McCabe at University of St. Andrews in St. Andrews, Fife, UK, were the original editors of CATCF. Volumes I (1992) through VI (1997) were funded by the Mathematical Institute of the University of Southern Colorado with contributions from the Centenary Fund of the Edinburgh Mathematical Society used for Volume III in 1994. No journal was published in 1998.

In 1999, Cathy Bonan-Hamada and Philip Gustafson of Colorado Mesa University in Grand Junction, Colorado, USA, and Lyle Cochran of Whitworth College in Spokane, Washington, USA, became the editors of CATCF. From 1999-2007, Volumes VII through XV of CATCF were published in the original format with Volumes VII through XI funded by the School of Natural Sciences and Mathematics at Mesa State College and Volumes XII through XV funded by the Department of Computer Science, Mathematics and Statistics at Mesa State College.

Advances in electronic communication have changed the way we share information. In January, 2009, the editors decided to move Volume XVI and subsequent volumes of CATCF to an exclusively electronic format, partly in response to increasing costs of publication and mailing of a paper journal. While the hardcopy volumes will be missed, an online CATCF offers a more dynamic way of sharing our announcements and reports with each other, which in turn helps CATCF fulfill its "Communications" mission.