# Proof - Legendre polynomials

by JiriV
Tags: legendre polynomials
 P: 2 Following relation seems to hold: $\int^{1}_{-1}\left(\sum \frac{b_{j}}{\sqrt{1-μ^{2}}} \frac{∂P_{j}(μ)}{∂μ}\right)^{2} dμ = 2\sum \frac{j(j+1)}{2j+1} b^{2}_{j}$ the sums are for j=0 to N and $P_{j}(μ)$ is a Legendre polynomial. I have tested this empirically and it seems correct. Anyway, I would like to have i) either a proof, or ii) a reference in a book, by which it is obtained easily. Do you have some suggestions? Thank you.