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    Radius of convergence of binomial series for fixed complex x

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    The generalized binomial coefficient for z in C (complex) and k = 0, 1, 2, ... is
    1 if k = 0 and

    ( k )
    ( z ) = [z(z-1) ... (z - k +1)] / k!

    if k >=1. For a fixed value of s in C we define the binomial series

    B_s*(z) = sum of n=0, ^infinity, ( s )
    ( n ) z^n

    Find the radius of convergence of B_s.

    See the formatted question attached.

    © BrainMass Inc. brainmass.com October 10, 2019, 5:26 am ad1c9bdddf
    https://brainmass.com/math/real-analysis/radius-convergence-binomial-series-fixed-complex-505200

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    Solution Summary

    In this solution, we show that the radius of convergence of the binomial series is 1 for all complex values of its argument.

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