How to Express the Product of Two Legendre Polynomials?

[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!

 

[soener]

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!

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