1. ## complex analysis

Hey guys.
I have two paths, and I need to proof the thing in red.
They give a tip due, they say to show first that the equation in green is correct and then using Taylor development, to proof the red equation.
I'm still in the first phase, in the green equation. I know it got something to do with Cauchy's integral formula but I cant see how...
Any idea guys?

Thanks a lot.

2. Consider the poles of $\displaystyle \frac{e^iz}{z^2+a^2}$ in the complex plane. What are the residues, and which ones are enclosed in your contour (a semi-circle of radius R in the upper half plane)?

--Kevin C.

3. Originally Posted by TwistedOne151
Consider the poles of $\displaystyle \frac{e^iz}{z^2+a^2}$ in the complex plane. What are the residues, and which ones are enclosed in your contour (a semi-circle of radius R in the upper half plane)?

--Kevin C.
I'm sorry but I'm not familiar with this terms (residues and such) because of my English.
Anyway, this is what I did (in the pic) and I used Cauchy's integral formula to calculate the integral but I'm not sure what it gave me.
I can't see how I can prove the equation in green using these.
Can I get some more tips?

Thanks a lot.