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It is stated that the associated Legendre functions change their sign n-m times in the interval -1 <= t <= 1, where t = cos(theta)...

P_{nm}(t) = {1/(2^{n}n!)}(1 - t^{2})^{m/2}D^{n+m}(t^{2}- 1)^{n}... Associated Legendre function

I can see how this number arises having differentiated (t^{2}- 1)^{n}, n+m times. But this is then multiplied by a factor of (1 - t^{2})^{m/2}, which is a polynomial in t of degree m.

So multiplying both polynomials you have a polynomial of degree [2n - (n+m)] + [m] = n

Where have I gone wrong in my understanding of this?

Thanks

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# Legendre's associated function - number of zeros?

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