Proof of a partial fraction theorem

Kinsama
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I've been looking all over the net since yesterday for a PROOF of a theorem called the "heaviside method" it involves partial fractions and itegration of such. If anyone could show me a proof of it or send me a link of it I would gladly appreciate it, thanks!
 
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Of what, specifically, do you want a proof?

P.S. if you have an algorithm that does something, that is a proof that you can do that something.
 
i want a proof of a theorem called the Heaviside Method, my book tells how to do it, but i need a proof of it for class and its almost impossible to find.
 
Well, if you need it for class, shouldn't you prove it yourself? :-p And I don't even know the theorem you're trying to prove -- I can find references to the algorithm called "Heaviside's method", but you can't prove an algorithm. (The very idea is nonsensical)

My best guess is that you want a proof that the algorithm works as advertised, and I've already given you a hint: just prove that the output of the algorithm is what it claims to be
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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