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

By Kenneth S. Berenhaut, Edward E. Allen and Sam J. Fraser


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

Year: 2006
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