Contour Integration: Rules and Limits

[jenga42]

I'm trying to do a trigonometric type contour integration... one with limits of integration between -Pi and Pi. Is there a rule about what the integrand has to look like?

Eg can I do this (I've converted it into z's):

int( f(z)/( (z-z1)^2 (z-z2)^2 ) ,z)

...can f(z) be any function?

And is it okay for the original limits to be from -Pi to Pi rather than the normal 0 to 2*Pi

Thanks!

 

[Gib Z]

f(z) can't be any function, the number and type of singularities it has around the region of integration can cause the integral to be ill-defined. Also, the limits should not matter, but if this is a contour integral, what is the counter? You define bounds like a normal integral.

 

[jenga42]

Thanks for replying...

I should have written "if f(z) doesn't have any singularities, can it be any function?" .. can it?

Thanks