Understanding Eigenvalues and the Role of Sigma in Integrals

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[URGENT] another Eigenvalue problem

Homework Statement


[PLAIN]http://img99.imageshack.us/img99/1762/222n.png


Homework Equations


N/A


The Attempt at a Solution


I've no clue what's going on for this one. What does that function even do anyway?
 
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On a side note, what is sigma in the integral?
 

Thread 'Finding the nth roots of a complex number'

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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