Discrete Dynamics in Nature and Society
Volume 2006 (2006), Article ID 40270, 18 pages

Bounds on coefficients of reciprocals of formal power series with rapidly decreasing coefficients

Kenneth S. Berenhaut, Edward E. Allen, and Sam J. Fraser

Department of Mathematics, Wake Forest University, Winston-Salem 27109, NC, USA

Received 8 August 2006; Revised 19 September 2006; Accepted 26 September 2006

Copyright © 2006 Kenneth S. Berenhaut et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper studies reciprocals of formal power series whose coefficients are monotone and bounded by a geometrically decaying sequence. Explicit and applicable, optimal decay rates are provided for the coefficients of the reciprocal series in terms of the parameters of the geometric bound. The results imply a best possible lower bound on the zeros of the series being considered.