How does one arrive at the equation(adsbygoogle = window.adsbygoogle || []).push({});

$$\bigg( (1-z^2) \frac{d^2}{dz^2} - 2z \frac{d}{dz} + l(l+1) - \frac{m^2}{1-z^2} \bigg) P(z) = 0$$

Solving this equation for ##P(z)## is one step in deriving the spherical harmonics "##Y^{m}{}_{l}(\theta, \phi)##".

The problem is that the book I'm following doesn't show how to arrive at the above equation. It shows how to arrive at it only for the special case ##m=0##.

I've tried googling "Associate Legendre's equation" and "Legendre's general equationderivation" but it seems there's no such derivation on web.

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# I Spherical harmonics

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