Prove g(z) = 1/(2*pi*i) int_c f(s)ds/(s-z) is analytic? How can I with an integral?

1. Apr 22, 2007

laura_a

1. The problem statement, all variables and given/known data

My text book has this question

f is continuous on C which is a simple closed contour...

Prove g(z) = 1/(2*pi*i) int_c f(s)ds/(s-z) is analytic?

I understand that you use Cauchy-Riemann proof for analytic functions, but how do I find the derivatve of a function that has an integral inside of it? Any suggestions?

2. Relevant equations

I thought maybe somehow I'd have to use the Cauchy Integral formula, but what version of it should I use? and should I even use that - the only reason I think that is that is the question in the text book after the Cauchy Integral topic! :)

3. The attempt at a solution

I'm not sure where to start because I dont know how to differentiate the funciton because of the integral there and not sure how to get rid of it! :yuck:

2. Apr 22, 2007

siddharth

Is that exactly how the question is stated? Does it say that f is continuous on C, or does it say f is analytic on and inside C?