Contour Integration: Rules and Limits

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SUMMARY

The discussion centers on the rules and limits of contour integration, specifically regarding the integrand function f(z) and its singularities. It is established that f(z) cannot be any function; the presence and type of singularities in the region of integration can render the integral ill-defined. Additionally, while the limits of integration can be from -π to π, the nature of the contour must be clearly defined to ensure proper evaluation of the integral.

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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!
 
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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.
 
Thanks for replying...

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

Thanks
 

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