
<div class="eqn">
<img src="eqn/spherharm6.png" alt="[eqn]"><!--MATH
\begin{equation*}
Y_{L,M}(\theta,\phi) =
\sqrt{2}
\sqrt{\frac{(2L+1)}{4\pi}\frac{(L-|M|)!}{(L+|M|)!}}
P_L^{|M|}(\cos\theta)
\sin(|M|\phi)
\end{equation*}
-->
</div>

<p>
These expressions do not include the Condon-Shortley phase, also not in the associated Legendre polynomials.
</p>

<p>
Both the set of complex spherical harmonics and the set of real-valued spherical harmonics defined by the above expressions are orthonormal sets.
</p>

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