Let C denote the circle |z| = 1, taken counterclockwise, and use the following steps to show that:
int(exp(z + 1/z) dz) = i2pie sum(1/ (n!(n + 1)!)
1) By using the Maclaurin series for e^z, write the above integral as
sum(1/n! int(z^n exp(1/z) dz) )
2) Apply Cauchy's residue theorem to evaluate the integrals above.© BrainMass Inc. brainmass.com March 4, 2021, 11:57 pm ad1c9bdddf
We compute a class of contour integrals using Cauchy's residue theorem as well as the MacLaurin series of the integrands.