## Spherical Harmonics

In solving the 3D hydrogen atom, we obtain a spherical harmonic, Y such that,
$$Y_{lm}(\theta,\phi) = \epsilon\sqrt{\frac{(2l+1)}{(4\pi)}}\sqrt{\frac{(l-|m|)!}{(l+|m|)!}}e^{im\phi}P^m_l(cos \theta)$$
where $$\epsilon = (-1)^m$$ for $$m \geq 0$$ and $$\epsilon = 1$$ for $$m \leq 0$$.
In quantum, m = -l, -l+1, ..., l-1, l.
But according to the formula above, when m = l, we should have zero and not a finite value, since $$l - |m| = 0$$. Which means the wavefunction should be zero when m = l.
Where did I go wrong?
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 Recognitions: Homework Help Science Advisor The factorial of 0 is 1. :)

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