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Many special functions appear as solutions of differential equations or integrals of elementary functions. Most special functions have relationships with representation theory of Lie groups.

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Divergence of conformal Killing vector fields on $S^2$ and the spherical harmonics

Can anyone think of a conformal Killing vector field $W$ on $S^2$ with the round metric that is not Killing such that its divergence is $L^2$-orthogonal to the spherical harmonics with $\ell = 1$? One …
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