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(Solved): Problem 1: For the following functions, find the Laurent series around the singularity; you may give ...
Problem 1: For the following functions, find the Laurent series around the singularity; you may give your
answer by using sigma notation, or writing the first four nonzero terms. Are the singularities removable,
poles, or essential? If it is a pole, give the order.
(a) zsin((1)/(z)).
(b) (cos(z-i)-1)/((z-i)^(2)).
(c) (sin(z)-1)/(z^(3)).