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Oct 14, 2016 at 9:11 comment added v217 I think this question is related to the question of a Fourier invariant (up to scaling) representation of spherical harmonics on the surface of the unit sphere. Something like the Fourier invariant (up to scaling) Hermite polynomials for the surface of the unit sphere. I am not as mathematically sophisticated, but I think the answer is Laguerre polynomials expanded in the usual legendre polynomials?
Jul 24, 2014 at 17:31 history edited Francois Ziegler CC BY-SA 3.0
Restored 1831 reference (since it is referred to in a comment)
Jul 24, 2014 at 17:17 vote accept Francois Ziegler
Jul 24, 2014 at 17:17 history edited Francois Ziegler CC BY-SA 3.0
Consolidated 2 answers
Nov 25, 2013 at 0:32 history edited Francois Ziegler CC BY-SA 3.0
added 197 characters in body
Nov 24, 2013 at 22:30 history edited Francois Ziegler CC BY-SA 3.0
Add refs to Burkhardt, Ostrogradsky, Poisson
Nov 24, 2013 at 14:21 history edited Francois Ziegler CC BY-SA 3.0
Stress remaining open question
Nov 24, 2013 at 7:27 history answered Francois Ziegler CC BY-SA 3.0