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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums | Science Articles, Homework Help, Discussion**