Legendre Funcs: Homework & Equations Explained

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Homework Statement



Hi everyone, I am having issues understanding how Legendre functions work especially the recursion and what the subscripts mean in general. I am attempting to make a program to compute the legendre functions Pnm(cos(theta)) and the normalized version and then verifying it by plotting 4 normalized legendre functions.

I don't understand what to do with these equations to get to what I'm attempting to do they just confuse me to no end.

Homework Equations



http://img14.imageshack.us/img14/5976/legendre.png

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I'm pretty sure I have to make a function to start with the original equation and then recursively go down. What do the subscripted n/m mean I'm confused on that as well xD
 
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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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