I want to prove orthogonality of associated Legendre polynomial.(adsbygoogle = window.adsbygoogle || []).push({});

In my text book or many posts,

[tex]\int^{1}_{-1} P^{m}_{l}(x)P^{m}_{l'}(x)dx = 0 (l \neq l')[/tex]

is already proved.

But, for upper index m,

[tex]\int^{1}_{-1} P^{m}_{n}(x)P^{k}_{n}(x)\frac{dx}{ ( 1-x^{2} ) } = 0 (m \neq k)[/tex]

is not proved.

So, I tried to prove it using same method for the first case.

But I could not prove it.

Will anyone show me a hint or online reference?

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# Proof of orthogonality of associated Legendre polynomial

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