Complex analysis fourier series

[Dassinia]

Hello,

Homework Statement

Develop in Fourier series 1/cos(z) and cotan(z) for Im(z)>0

Homework Equations

The Attempt at a Solution

I really don't know how to do this, i was looking at my notes and we just saw Fourier transform and there is no example for complex functions.
I was thinking to develop cos(z) in exponential form and simplify and then i don't know what to do if someone can "guide" me it'd be great !
Thanks

 

[vela]

Is that the entire problem statement word for word? It doesn't make sense to me as written.

 

[Dassinia]

Find the Fourier series of the functions 1/cos(z) and cotan(z) for Im(z)>0
this is it.

Thanks

 

[vela]

Do you know what a Fourier series is? If not, that would be the place to start.

 

[Dassinia]

Yes I know and I used to calculate Fourier series for real functions in a previous course.
But for this one z=x+iy so we have two variables so I don't know if I have to calculate the Fourier series according to one of them or both ?

 

[vela]

Well, there's this: http://en.wikipedia.org/wiki/Fourier_series#Fourier_series_on_a_square

That could be a starting point, but your problem seems a bit complicated because your functions don't appear periodic in both x and y.