Discrete Dynamics in Nature and Society 
Volume 2006 (2006), Article ID 40270, 18 pages
doi:10.1155/DDNS/2006/40270

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

Abstract

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.