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
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.