Spherical Harmonics

touqra

In solving the 3D hydrogen atom, we obtain a spherical harmonic, Y such that,
[tex] 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)[/tex]
where [tex]\epsilon = (-1)^m [/tex] for [tex] m \geq 0 [/tex] and [tex] \epsilon = 1 [/tex] for [tex] m \leq 0 [/tex].
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 [tex] l - |m| = 0 [/tex]. Which means the wavefunction should be zero when m = l.
Where did I go wrong?

Tide

The factorial of 0 is 1. :)