Laurent series 0 < |z-3| < 3

Question

I wanna check my laurent series exercises on Mathematica, but can't seem to find a command or program to achieve the result of such type of interval.

$f(z)=\frac{1}{(z-3) z},\\1<|z-3|<3$

The command Series[] won't let me use $z-3$ as the expansion variable.

Please, look at the following reference: http://mathematica.stackexchange.com/questions/23578/laurent-series-expansion?rq=1 — Gilmar Rodriguez Pierluissi, Oct 18 '16 at 17:06

score 6 · Accepted Answer · answered Oct 18 '16 at 16:53

6

If you want to expand your series about the point z = 3 you can do this:

Series[1/(z - 3)/z, {z, 3, n}]

Just change n to be the number of terms you want in the expansion.

answered Oct 18 '16 at 16:53

dan7geo

3

You can use SeriesCoefficient too and not need to replace n with an explicit integer. – Greg Hurst Oct 18 '16 at 17:45
1

But wouldn't it be the same as calculate the series for 0 < |z| <3? – Vinholi Oct 18 '16 at 18:42

1 Answers1