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

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.