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trickae
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In https://www.amazon.com/dp/0139078746/?tag=pfamazon01-20 - residues is introduced as an exercise at the end of a chapter and that's it! (or it may resurface in a later chapter),
My question is that saff and snider looks at it as the numerator of the partial fraction exapansion of a polynomail fraction.
But in Schaums series we have a nice little function like this:
where the term in red is the differential operator and the order is determined by k-1
so what's this used for? which method is right? why choose one method over the other? And what is it beside the sum of all the residues at the singularities = the integral of the function that contains it - i.e. f(z) ?
sorry if this is a silly question.
My question is that saff and snider looks at it as the numerator of the partial fraction exapansion of a polynomail fraction.
But in Schaums series we have a nice little function like this:
Code:
a = lim 1/(k-1)! . [color=red](d^(k-1) /dz^(k-1)) [/color] {(z-a)^k f(z)}
z->a
where the term in red is the differential operator and the order is determined by k-1
so what's this used for? which method is right? why choose one method over the other? And what is it beside the sum of all the residues at the singularities = the integral of the function that contains it - i.e. f(z) ?
sorry if this is a silly question.
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