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I'm trying to prove the orthogonality of associated Legendre polynomial which is called to "be easily proved":

Let

[tex]P_l^m(x) = (-1)^m(1-x^2)^{m/2} \frac{d^m} {dx^m} P_l(x) = \frac{(-1)^m}{2^l l!} (1-x^2)^{m/2} \frac {d^{l+m}} {dx^{l+m}} (x^2-1)^l [/tex]

And prove

[tex]\int_{-1}^1 P_l^m(x)P_{l'}^{m'} (x)dx = \frac{2}{2l+1} \frac {(l+m)!} {(l-m)!} \delta_{ll'} \delta_{mm'} [/tex]

Though it should be easily proved, I don't know how. When [tex]m = m' = 0,[/tex] it's unassociated Legendre polynomials and it's not difficult (I'll post in the next message).

Will anyone show me a hint or online reference? I don't need exact value (because won't be difficult). All I want to prove is orthogonality.

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# Proof of orthogonality of associated Legendre polynomial

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