How we solve those?

Printable View

- May 25th 2009, 12:44 PMNaNacomplex integral
How we solve those?

- May 25th 2009, 06:15 PMartvandalay11example of Cauchy's Integral Formula
For the first one, if , then we can use Cauchy's Theorem to change the curve to a point through a homotopy and the integral over a point is zero.

For n=-1 use Cauchy's Integral formula to conclude the answer is

For then we have to use Cauchy's General Integral Formula which is where is the n-th derivative of f(z) evaluated at the point a

So...

for k=-n and by Cauchy's Integral formula this integral is

but f(z)=1 in this case, so the k-1 derivative of 1 is 0 (as k-1 is always at least 1) and anything times 0 is 0. - May 25th 2009, 06:44 PMartvandalay11

Now Cauchy's integral formula states:

where is the n-th derivative of f(z) evaluated at the point a

So where f(z)=

I'll leave it to you to find the second derivative, plug in z= and multiply it by