In https://www.amazon.com/Fundamentals...6816057?ie=UTF8&s=books&qid=1177661695&sr=8-1 - residues is introduced as an exercise at the end of a chapter and thats it! (or it may resurface in a later chapter),(adsbygoogle = window.adsbygoogle || []).push({});

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-1Code (Text):

a = lim 1/(k-1)! . [color=red](d^(k-1) /dz^(k-1)) [/color] {(z-a)^k f(z)}

z->a

so whats 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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# What exactly is a residue - what are its applications[complex analysis]

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