1. 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.

2. Hello,

Since $\displaystyle w\in\mathbb{C}\backslash\mathcal{C}$, the function $\displaystyle f(z)=\frac{\sin(z)}{(z-w)^2}$ has no singularity within $\displaystyle \mathcal{C}$
Hence it's a holomorphic function in $\displaystyle \mathcal{C}$ and we can apply Cauchy's integral theorem...

Cauchy's integral formula wouldn't work because w is not within $\displaystyle \mathcal{C}$

3. Hi, I dont quite get what you mean

I understand that w covers all complex number except C

What does the C stand for?

4. 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 $\displaystyle w$ is in the domain, $\displaystyle g(w)=?$
(2) else if $\displaystyle w$ is outside the domain, $\displaystyle g(w)=?$

5. Originally Posted by luobo
Two cases:
(1) If $\displaystyle w$ is in the domain, $\displaystyle g(w)=?$
(2) else if $\displaystyle w$ is outside the domain, $\displaystyle g(w)=?$
Hi luobo

Is this what you meant?

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

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

Am I correct in doing so?