13. (5 pts) For analytic functions f, the basic Cauchy Integral Formula states: 5.10 f(w) dw = 2nif(), w 2 = for a simpl

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13 5 Pts For Analytic Functions F The Basic Cauchy Integral Formula States 5 10 F W Dw 2nif W 2 For A Simpl 1 (53.31 KiB) Viewed 27 times

13. (5 pts) For analytic functions f, the basic Cauchy Integral Formula states: 5.10 f(w) dw = 2nif(), w 2 = for a simple closed contour C, positively oriented with z in its interior. Assuming this formula holds, as the “n=0" case, and also assuming that the equation & SK(z,w)dw = Sc &K(z,w)dw may be used when needed, give a proof using induction and the power rule for derivatives of the general Cauchy Integral Formula for n = 1,2,3,... f(w) 2πί (w - 2)+1 n! Jawa dw -f(n)(z). = secu).