# Product of Legendre Polynomials

1. Feb 21, 2008

### Repetit

Hey!

Could someone please help me find out how to express the product of two Legendre polynomials in terms of a sum of Legendre polynomials. I believe I have to use the recursion formula

$$(l+1)P_{l+1}(x)-(2l+1) x P_l(x) + l P_{l-1}(x)=0$$

but I am not sure how to do this. What is basically want to do is

$$P_n(x) P_m(x) = \sum\limits_i c_i P_i(x)$$

I hope my question is understandable.

Thanks!

2. Aug 11, 2011