Bounds on coefficients of reciprocals of formal power series with rapidly decreasing coefficients. (28th December 2006)

• Record Type: Journal Article
• Authors: Berenhaut, Kenneth S.; Allen, Edward E.; Fraser, Sam J.
• Is Part Of: Discrete dynamics in nature and society. Volume 2006(2006)
• Publication Date: 2006-12-28
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/DDNS/2006/40270
• Languages: English
• ISSNs: 1026-0226

Abstract

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.