= Gaunt integral
{c}
{title2=$\mathcal G^{\ell_1\ell_2\ell_3}_{m_1m_2m_3}=\int Y_{\ell_1m_1}Y_{\ell_2m_2}Y_{\ell_3m_3}\,d\Omega$}
= Gaunt coefficient
{c}
{synonym}
The integral of three <spherical harmonics> on the sphere. In the conventional complex basis it is real and equals a product of two <Wigner 3j symbols> and $\sqrt{(2\ell_1+1)(2\ell_2+1)(2\ell_3+1)/(4\pi)}$. It vanishes unless the multipoles satisfy a triangle condition, $\ell_1+\ell_2+\ell_3$ is even, and $m_1+m_2+m_3=0$. It carries the angular geometry of the <reduced CMB bispectrum>.
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