Bounds on coefficients of reciprocals of formal power series with rapidly decreasing coefficients
Kenneth S. Berenhaut, Edward E. Allen, Sam J. Fraser · Discrete Dynamics in Nature and Society · 2006
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.