8.1 • THE RESIDUE THEOREM 293• EXAMPLE 8.3 Evaluate f exp(;) dz.
ct(o)
Solution In Example 8.1 we showed that the residue of f (z) = exp (D at
zo = 0 is Res[/, OJ = 2. Using Equation (8-2), we get
j exp (;) dz = 2?ri Res[/ , OJ = 4?ri.
Ci(O)
The calculation of a Laurent series expansion is tedious in most circum-
stances. Since the residue at zo involves only the coefficient a_ 1 in the Laurent