- #1
wam_mi
- 81
- 1
Homework Statement
Find the Principle part of the Laurent Expansion of f(z) about z=0 in the region
0 < mod z < 1, where f(z) = exp(z) / [(z^2)*(z+1)]
Homework Equations
1/(1-z) = Summation (n = 0 to n = infinity) { z^n}
The Attempt at a Solution
First, by using partial fraction,
I got f(z) = exp(z) {-1/z + 1/(z^2) + 1/(z+1)}
Then f(z) = exp (z) {1/ (-1+1+z) + 1/ (-1+1+(z^2)) + (1/(z+1) }
Since the question were only after the principle parts, so I ignore 1/(z+1) term
Basically I need to evalute
exp (z) { 1/ (-1+1+z) + 1/ (-1+1+(z^2)) }
Is this step right?
Then I tried to do the following,
and I got something like
exp (z) { - summation (1/(1+z))^(n+1) + summation (1/(1+z^2))^(n+1)}
But is this right?
Thanks a lot!