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    Bounds for analytic functions

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    If p(z)=a0+a1z+.....+anz^n ia a polynomial and max|p(z)|=M for |z|=1, show that each coefficient ak is bounded by M.

    Note:(a0 means a subscript 0, a1z means a subscript 1 times z, anz^n means a subscript n times z to the n power, and ak means a subscript k)

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    Please see the attachment.

    , , show that for all ...

    Solution Summary

    This is a proof of bounds for an analytic function using Cauchy formula.