(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let f and g ve analytic functions inside and on a simple connected contour [itex] \Gamma [/itex]. If f(z) = g(z) for all z on [itex] \Gamma [/itex], prove that

If f(z) = g(z) for all z inside [itex] \Gamma [/itex]

2. Relevant equations

[tex]

f(z_{0}) = \int_{\Gamma}\dfrac{f(z)}{z-z_{0}}dz [/tex]

if f is analytic in a simple connected domain containing [itex] \Gamma [/itex] and [itex] z_{0} [/itex] is a point insinde [itex] \Gamma [/itex].

3. The attempt at a solution

I know I must (?) prove that [itex]f(z_{0}) = g(z_{0}) [/itex] for all z_0, but i have no idea how to use the fact that f and g are equal on all point on [itex] \Gamma [/itex], I have no Lemma or Theoreme for this in my book (I am not allowed to use the theory of bounds for analytical functions, just Cauchy's integral formula)

Can someone give me a small hint ? =)

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# Homework Help: Proof using Cauchy's integral formula

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