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The real-form spherical harmonic basis functions (with θ the planetocentric co-latitude in the COM frame) are:
$$\begin{array}{c}{Y}_{{\ell }0}(\theta ,\lambda )=\sqrt{\frac{2{\ell }+1}{4{\rm{\pi }}}}{P}_{{\ell }0}(\cos \theta ),\\ {Y}_{{\ell }m}^{{\rm{c}}}(\theta ,\lambda )=\left\{\begin{array}{cc}\sqrt{\frac{(2{\
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