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Math Help - <please help me>

  1. #1
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    <please help me>

    suppose that f and g are continuous functions on a closed bounded region R and let D be the interior of R if f and g are analytic throughout D with f(z)=g(z) for all z in the boundary of R
    prove that :
    f(z)=g(z) for all z in R
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  2. #2
    MHF Contributor chisigma's Avatar
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    Let C the line that limits the region D. If f(*) is analytic inside and on C and a a point internal to C is...

    f(a)= \frac{1}{2\pi i} \oint_{C} \frac{f(z)}{z-a} dz (1)

    If f(*) and g(*) are both analytic and on C is f(z)=g(z), then for the (1) the same holds in any point of D...

    Kind regards

    \chi \sigma
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