Question #236288

4)Find the Laurent series expansion of the function 2z/ z²+2z-3 in the region 2<|z+1| <4.

Explain the problem with step by step process?

Expert's answer

The Taylor series is the Laurent expansion about z = 0 because the function is analytic there and has radius of convergence 1.

The expansions about i and -i have one term with a power -1. As z^2 + 1 = (z-i)(z+i) you can multiply your function by one of the factors, find the Taylor series, then divide all terms by that factor. And voila! there’s a Laurent series.

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