On 5/28/07, Hydra Liu <yuliu at shao.ac.cn> wrote:
>
> Sorry, I forgot writing the assumption that n1 < n2.
> In fact, P[n](x) is Legendre polynomials.
> Under the assumption above, n1 will not appear on the RHS.
>>>
P[n1](x) * P[n2](x) = sum( H(l) * P[l](x), l, 0,n2), where H() are
coefficients
<<<
n1 must appear somehow. Otherwise:
P[n1](x) = sum( H(l) * P[l](x), l, 0,n2)/ P[n2](x)
for all n1 < n2, and therefore P[i](x) = P[j](x) for all values of i, j.
And this probably leads to a contradiction. There is something missing
here.
You also don't say what you want to do with this identity. Do you want to
simplify expressions involving products of P's? Do you want to determine
P[i] for various i?
-s