from my understanding we use residue theory when we have poles.(adsbygoogle = window.adsbygoogle || []).push({});

The question i have is

if f(z) = 1/(1-Z^2) has two poles at 1, -1 each of order 1

then does

Res[f(z),-1] = lim as z -> -1 of (z+1)(f(z)) = -1/2

if we have a pole of order 1 then

Res[f(z),z0] = lim as z -> z0 of (z - z0)f(z)

or does

Res[f(z),-1] = lim as z -> -1 of (z+2)(f(z)) = undefined

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# Anyone familiar with residue theory

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