A fundamental theorem due to the French mathematician Augustin Cauchy extablishes that if is analytic in a region inside a closed path is...

(1)

Now if is analytic in the whole complex plane [i.e. is anentire function...] the (1) is valid independently from , and that means that, if we devide in two parts, one coming from to and the other coming back from to is...

(2)

... and that means that depends only from and anddoesn't dependfrom the path connecting and ...

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