Worked Example Calculating Residues Example z By expanding as a Taylor series we see that z has a Laurent expansion about given by Hence the residue is the coecient of
Alternatively we note that has a pole of order 3 at 0 so we can use the general formula for the residue at a pole res 0 lim 2 lim Example 1 We have already calculated the Laurent expansion of 1 at 1 so the residue is e 2 Alternatively we use
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