The following command is returned unevaluated. The answer is well known to be related to Wigner's 3j Symbol which is also a defined function in Mathematica.

    SphericalHarmonicY[l, -m, θ, ϕ] SphericalHarmonicY[1, 0, θ, ϕ] *
     SphericalHarmonicY[l + 1, m, θ, ϕ] Sin[θ],
    {ϕ, 0, 2 π}, {θ, 0, π}] 
  • $\begingroup$ People here generally like users to post code as Mathematica code instead of images or TeX, so they can copy-paste it. It makes it convenient for them and more likely you will get someone to help you. You may find this this meta Q&A helpful $\endgroup$
    – Michael E2
    Feb 1, 2018 at 1:52
  • $\begingroup$ Your Y_1 is undefined (for instance). $\endgroup$ Feb 1, 2018 at 1:52
  • $\begingroup$ Try to add constraints for m and l, and/or substitute their definition in terms of the associate Legendre polynomials and complex exponentials... $\endgroup$ Feb 1, 2018 at 12:33
  • $\begingroup$ Adding the usual constraints on m and l does not make any difference. I don't see why I should have to write SphericalHarmonics in terms of Legendre polynomials, that is something the algorithm has to do internally. $\endgroup$ Feb 1, 2018 at 18:16


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