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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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... (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

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