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

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  • Kenneth S. Berenhaut
  • Edward E. Allen
  • Sam J. Fraser

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.

Suggested Citation

  • Kenneth S. Berenhaut & Edward E. Allen & Sam J. Fraser, 2006. "Bounds on coefficients of reciprocals of formal power series with rapidly decreasing coefficients," Discrete Dynamics in Nature and Society, Hindawi, vol. 2006, pages 1-18, December.
    • Handle: RePEc:hin:jnddns:040270
    DOI: 10.1155/DDNS/2006/40270
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