Thread: Laurent Series

Hi guys,

I need help with a problem. we need to find the Laurent series in this problem.

we have the partial fraction

f(z) = 4/z((1/1+z) + (1/2-z). Now it says, for 0 < |z| < 1, we expand each of the fractions in the parenthesis in powers of z. This gives:

f(z) = -3 + 9z/2 - 15z^2/4 + 33z^3/8 + ...... + 6/z

can you please tell me how are we getting this expansion?? i really need your help. i have a final coming up.

thanks a lot for your support.

Originally Posted by sonaiarko

Hi guys,

I need help with a problem. we need to find the Laurent series in this problem.

we have the partial fraction

f(z) = 4/z((1/1+z) + (1/2-z). Now it says, for 0 < |z| < 1, we expand each of the fractions in the parenthesis in powers of z. This gives:

f(z) = -3 + 9z/2 - 15z^2/4 + 33z^3/8 + ...... + 6/z

can you please tell me how are we getting this expansion?? i really need your help. i have a final coming up.

thanks a lot for your support.

Use a geometric series expansion like this