Laurent series: can calculate myself, just need a quick explanation how

[Mathmos6]

Homework Statement

Hi all,

I've just calculated the first three nonzero terms of the Laurent series of 1/(cos(z)-1) in the region |z|<2pi, and now I've been asked to 'find the three non-zero central terms of the Laurent expansion valid for 2pi<|z|<4pi' - firstly, what does it mean by 'central terms', and secondly, how do I calculate an expansion valid in an annulus? I have no idea how to expand except for in a ball |z-a|<r, unless I'm being slow here (very possible)! Perhaps the second question will answer the first for me anyway - thanks very much for the help,

M

 

[vela]

"Central" probably means the terms around the z⁰ term. The Laurent series can have powers of z that go from -infinity to +infinity, so the "center" would be the n=0 term.