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    Cauchy- Hadamard Theorem on power series.

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    Complex Variable

    Cauchy- Hadamard Theorem :-
    ∞
    For every power series &#8721; anzn there exist a number R, 0 &#8804; R < &#8734;
    n=0

    called the radius of convergence with the following properties:

    (i) The series converges absolutely for every |z| < R
    (ii) If 0 &#8804; &#961; < R, the series converges uniformly for |z| &#8804; &#961;
    (iii) If |z| > R, the terms of the series are unbounded and the series is consequently divergent.

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    https://brainmass.com/math/real-analysis/cauchy-hadamard-theorem-on-power-series-37237

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    Complex Variable

    Cauchy- Hadamard Theorem :-
    ...

    Solution Summary

    &#8734;
    This solution is comprised of a detailed explanation of the radius of convergence of the power series &#8721; anzn.
    n=0
    It contains step-by-step explanation for the following problem:
    Cauchy- Hadamard Theorem :-
    &#8734;
    For every power series &#8721; anzn there exist a number R, 0 &#8804; R < &#8734;
    n=0

    called the radius of convergence with the following properties:

    (i) The series converges absolutely for every |z| < R
    (ii) If 0 &#8804; &#961; < R, the series converges uniformly for |z| &#8804; &#961;
    (iii) If |z| > R, the terms of the series are unbounded and the series is consequently divergent.

    Solution contains detailed step-by-step explanation.

    $2.49

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