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variants of this functions
SphericalHarmonicY






Mathematica Notation

Traditional Notation









Polynomials > SphericalHarmonicY[n,m,theta,phi] > Integration > Indefinite integration > Involving functions of the direct function and elementary functions with respect to theta > Involving elementary functions of the direct function and elementary functions > Involving products of the direct function and trigonometric functions





http://functions.wolfram.com/05.10.21.0003.01









  


  










Input Form





Integrate[((n - k) (n + k + 1) - (m^2 - l^2)/Sin[\[CurlyTheta]]^2) Sin[\[CurlyTheta]] SphericalHarmonicY[k, l, \[CurlyTheta], \[CurlyPhi]] SphericalHarmonicY[n, m, \[CurlyTheta], \[CurlyPhi]], \[CurlyTheta]] == (l - m) Cos[\[CurlyTheta]] SphericalHarmonicY[n, m, \[CurlyTheta], \[CurlyPhi]] SphericalHarmonicY[k, l, \[CurlyTheta], \[CurlyPhi]] + (Sin[\[CurlyTheta]] (((Sqrt[Gamma[k - l + 1]] Sqrt[Gamma[k + l + 2]])/ (Sqrt[Gamma[k + l + 1]] Sqrt[Gamma[k - l]])) SphericalHarmonicY[n, m, \[CurlyTheta], \[CurlyPhi]] SphericalHarmonicY[k, l + 1, \[CurlyTheta], \[CurlyPhi]] - ((Sqrt[Gamma[n - m + 1]] Sqrt[Gamma[n + m + 2]])/(Sqrt[Gamma[n + m + 1]] Sqrt[Gamma[n - m]])) SphericalHarmonicY[n, m + 1, \[CurlyTheta], \[CurlyPhi]] SphericalHarmonicY[k, l, \[CurlyTheta], \[CurlyPhi]]))/ E^(I \[CurlyPhi])










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29





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