# Fourier Series Time Multiplication

1. Oct 22, 2007

### er0ck

I am stuck at one point in this problem (which is the main step):

The original problem is to find the Fourier Transfer of t^(n-1)e^(-$$\alpha$$*t)u_h

and I know that e^(-$$\alpha$$t)u_h(t) = 1/($$\alpha$$+j$$\omega$$)

I plug that into the general Time multiplication property and I get:

d^(n-1)/d$$\omega$$^(n-1)*[1/($$\alpha$$+j$$\omega$$)]
This is where I'm stuck.

I have the answer is equal to (n-1)!/($$\alpha$$+j$$\omega$$^2)^n
I apologize for the bad formating, this is my first time using physics forum. =/ Thanks in advance!