Question #231334

9)Find Laurent series expansion of the function 1/ z²+z-6 in the regions

1<|z-1 <4 and |z-1|> 4.

Expert's answer

From partial fraction

so on either annulus, it is enough to find the Laurent series expansions of the functions and and then combine them term by term.

If then note that

and the fact that |z|>2

|z|>2 implies that |2z

−1

|<1

|2z−1|<1. If you recall the geometric series formula,

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