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    Cauchy's integral formula and residue theorem

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    (See attached file for full problem description and embedded formulae)

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    Why can (1) be regarded as a special case of (2)?

    (1) Cauchy's Integral formula (no need to prove):
    is a simple closed positively oriented contour.
    If is analytic in some simply connected domain D containing
    and if is any point inside , then

    (2) Cauchy's Residue Theorem (no need to prove):

    is a simple closed positively oriented contour
    and is analytic inside and on except at the points
    inside , then

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    (See attached file for full problem description and embedded formulae)

    © BrainMass Inc. brainmass.com December 24, 2021, 5:25 pm ad1c9bdddf
    https://brainmass.com/math/integrals/cauchy-s-integral-formula-and-residue-theorem-46769

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    This shows a proof regarding Cauchy's Integral formula and Residue Theorem.

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