Editing Spherical harmonics (section)

=== Contraction rule ===
Another useful identity expresses the product of two spherical harmonics as a sum over spherical harmonics<ref>{{cite book | last1=Brink|first1=D. M.|last2=Satchler|first2=G. R.|title=Angular Momentum|publisher=Oxford University Press|page=146}}</ref>
<math display="block"> Y_a^{\alpha}\left(\theta,\varphi\right)Y_b^{\beta}\left(\theta,\varphi\right) = \sqrt{\frac{\left(2a+1\right) \left(2b+1\right)}{4\pi}}\sum_{c=0}^{\infty}\sum_{\gamma=-c}^{c}\left(-1\right)^{\gamma}\sqrt{2c+1}\begin{pmatrix}
a & b & c\\
\alpha & \beta & -\gamma
\end{pmatrix} \begin{pmatrix}
a & b & c\\
0 & 0 & 0
\end{pmatrix} Y_c^{\gamma}\left(\theta,\varphi\right). </math>
Many of the terms in this sum are trivially zero. The values of <math> c </math> and <math>\gamma</math> that result in non-zero terms in this sum are determined by the selection rules for the [[3j-symbol]]s.