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variants of this functions
SphericalHarmonicY






Mathematica Notation

Traditional Notation









Hypergeometric Functions > SphericalHarmonicY[lambda,mu,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/07.37.21.0003.01









  


  










Input Form





Integrate[((\[Lambda] - \[Kappa]) (\[Lambda] + \[Kappa] + 1) - (\[Mu]^2 - \[Nu]^2)/Sin[\[CurlyTheta]]^2) SphericalHarmonicY[\[Lambda], \[Mu], \[CurlyTheta], \[CurlyPhi]] SphericalHarmonicY[\[Kappa], \[Nu], \[CurlyTheta], \[CurlyPhi]] Sin[\[CurlyTheta]], \[CurlyTheta]] == (\[Nu] - \[Mu]) Cos[\[CurlyTheta]] SphericalHarmonicY[\[Lambda], \[Mu], \[CurlyTheta], \[CurlyPhi]] SphericalHarmonicY[\[Kappa], \[Nu], \[CurlyTheta], \[CurlyPhi]] + (Sin[\[CurlyTheta]] (((Sqrt[Gamma[\[Kappa] - \[Nu] + 1]] Sqrt[Gamma[\[Kappa] + \[Nu] + 2]])/(Sqrt[Gamma[\[Kappa] + \[Nu] + 1]] Sqrt[Gamma[\[Kappa] - \[Nu]]])) SphericalHarmonicY[\[Lambda], \[Mu], \[CurlyTheta], \[CurlyPhi]] SphericalHarmonicY[\[Kappa], \[Nu] + 1, \[CurlyTheta], \[CurlyPhi]] - ((Sqrt[Gamma[\[Lambda] - \[Mu] + 1]] Sqrt[Gamma[\[Lambda] + \[Mu] + 2]])/ (Sqrt[Gamma[\[Lambda] + \[Mu] + 1]] Sqrt[Gamma[\[Lambda] - \[Mu]]])) SphericalHarmonicY[\[Lambda], \[Mu] + 1, \[CurlyTheta], \[CurlyPhi]] SphericalHarmonicY[\[Kappa], \[Nu], \[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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