Following relation seems to hold:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\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}[/itex]

the sums are for j=0 to N and [itex]P_{j}(μ)[/itex] 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.

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# Proof - Legendre polynomials

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