I'm just learning Laurent series. Could someone help me with this:

Find the Laurent series for the function z/[(z+1)(z+2)] in the following regions:

|z| < 1, 1 < |z| < 2, and |z| < 2.

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- Apr 30th 2007, 11:18 AMspoon737Laurent Series
I'm just learning Laurent series. Could someone help me with this:

Find the Laurent series for the function z/[(z+1)(z+2)] in the following regions:

|z| < 1, 1 < |z| < 2, and |z| < 2. - Apr 30th 2007, 12:48 PMTD!
Laurent expansions about z = 0, I suppose?

With partial fractions, you can rewrite:

z/((z+1)(z+2)) = 2/(z+2) - 1/(z+1)

You can now use the known Taylor series for |z| < 1. Watch out, you'll need a subtle manipulation for the other intervals, in order to make sure that the Taylor series still converge.