# theorems on analytic extension

I am a probability student and I have forgotten much of complex analysis I have learnt when I was an undergraduate.

I have recently seen integrals evaluated using analytic extensions techniques when integrals are evaluated some certain value for a parameter (like in Fourier transform, for $\theta\in\mathbb{R}$, but we can extend the range the Fourier integral is valid for) but I have forgotten most of the results on analytic extension. Can someone give me a shortlist of theorem which would be useful.

I still vaguely remember how to do complex integration and I have reminded myself the Identity theorem. Is there anything people would suggest I should look at for things related to the above?

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jesus, I don't realise how many grammar erros/typos i make until I see the edits someone makes to my post... –  Lost1 Apr 12 at 23:33