The defintion of 'residue' of an which has a pole of order m in and is analytic elsewhere in a region around is ...
Now if is...
... where is analytic in the (1) gives to You...
Let be an isolated point of a function and suppose that , where is a positive integer and is analytic and nonzero at . By applying the extended form of the Cauchy integral formula to the function , show that .
I do not see how to do this. Our book says:
Since there is a neighborhood throughout which is analytic, the contour used in the extended Cauchy integral formula can be the positively oriented circle . How do I use this suggestion? I don't see that now. Thanks in advance.