Thread: Countour Integral

I have no idea where should I start. I have only learned line integration, Cauchy's Integral theorem and formula.

Please give me some hints on where should I begin. Do note that I have not learned very detail in this topic.

Hello,

Since , the function has no singularity within
Hence it's a holomorphic function in and we can apply Cauchy's integral theorem...


Cauchy's integral formula wouldn't work because w is not within

Hi, I dont quite get what you mean

I understand that w covers all complex number except C

What does the C stand for?

Originally Posted by wzseow

I have no idea where should I start. I have only learned line integration, Cauchy's Integral theorem and formula.

Please give me some hints on where should I begin. Do note that I have not learned very detail in this topic.

Two cases:
(1) If is in the domain,
(2) else if is outside the domain,

Originally Posted by luobo

Two cases:
(1) If is in the domain,
(2) else if is outside the domain,

Hi luobo

Is this what you meant?

1) If is in the domain, then I have to use Cauchy's Integral theorem and calculate the integral

2) If is outside of the domain, then g(w) = 0 from Cauchy's integral formula


Am I correct in doing so?