# Thread: Partial fraction expansion (z-transforms)

1. ## Partial fraction expansion (z-transforms)

Hi,
I have a function
Y(z)= 1/(1-z^-1)^3,
I used the convolution sum to get:-
y[n]= 1/2(n+2)(n+1)u[n]
But is it possible to expand Y(z) and evaluate y[n] directly using partial fractions or any other method?
Cheers

2. In case any one is interested:-

Using

A/(1-dz^-1)^m <--z--> [A(n-1)...(n+m-1)d^n/(m-1)!]u[n] for ROC |z|>d

which implies the answer is:
y[n]= 1/2(n+2)(n+1)u[n]

Can also be solved using the power series but harder to find a general representation..