= Scalar spheroidal harmonic
{title2=$S_{\ell m}(\theta;c),\quad c=a\omega$}
= Spin-zero spheroidal harmonic
{synonym}
A <scalar spheroidal harmonic> is a regular angular solution of $(\sin\theta\,S')'/\sin\theta+[c^2\cos^2\theta-m^2/\sin^2\theta+\Lambda]S=0$; with $e^{im\phi}$ it is smooth at both axes. For real $c$, regularity gives discrete eigenvalues $\Lambda_{\ell m}(c)$. At $c=0$ it reduces to the angular part of a <spherical harmonic>, with $\Lambda=\ell(\ell+1)$. The sign of the $c^2$ term distinguishes the convention used here.
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