Thread: Laurent Series

Find the laurent series on 2<|z|<3
f(z)=1/[(z^2)*(z-2)*(z+3)]

Originally Posted by scubasteve123

Find the laurent series on 2<|z|<3
f(z)=1/[(z^2)*(z-2)*(z+3)]

Around what value of z is the series to be found?

There isnt an indicated center. All the question says is "Find Laurent series expansion(in powers of z) that represents the function in the region 2<|z|<3

Originally Posted by scubasteve123

There isnt an indicated center. All the question says is "Find Laurent series expansion(in powers of z) that represents the function in the region 2<|z|<3

"(in powers of z)" means you find it around z = 0. So the centre is given. It helps if the whole question is posted.

I suggest writing the given function as where the partial fraction decomposition is left for you to finish.

Then expand each of and around z = 0. Then substitute etc.

eg. where you should recognise an infinite geometric series with (note that since .