Prove that under the conditions of Problem 2, f^(n)(a)=(n !)/(2 πi) (f(z))/((z-a)^n+1) d z n=0

Question

Prove that under the conditions of Problem 2, f^(n)(a)=(n !)/(2 πi) (f(z))/((z-a)^n+1) d z   n=0

Accepted Answer

Step 1: Start with the Cauchyu0027s integral formula for the nth derivative of a function. It states

Prove that under the conditions of Problem 2, $$ f^{(n)}(a)=\frac{n !}{2 \pi i} \oint_C \frac{f(z)}{(z-a)^{n+1}} d z \quad n=0,1,2,3, \ldots $$