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variants of this functions
SphericalHarmonicY






Mathematica Notation

Traditional Notation









Hypergeometric Functions > SphericalHarmonicY[lambda,mu,theta,phi] > Integration > Definite integration > Multiple integration





http://functions.wolfram.com/07.37.21.0011.01









  


  










Input Form





Integrate[Sin[\[CurlyTheta]] SphericalHarmonicY[Subscript[n, 1], Subscript[m, 1], \[CurlyTheta], \[CurlyPhi]] SphericalHarmonicY[Subscript[n, 2], Subscript[m, 2], \[CurlyTheta], \[CurlyPhi]] Conjugate[SphericalHarmonicY[Subscript[n, 3], Subscript[m, 3], \[CurlyTheta], \[CurlyPhi]]], {\[CurlyTheta], 0, Pi}, {\[CurlyPhi], 0, 2 Pi}] == Sqrt[((2 Subscript[n, 1] + 1) (2 Subscript[n, 2] + 1))/ (4 Pi (2 Subscript[n, 3] + 1))] ClebschGordan[{Subscript[n, 1], 0}, {Subscript[n, 2], 0}, {Subscript[n, 3], 0}] ClebschGordan[{Subscript[n, 1], Subscript[m, 1]}, {Subscript[n, 2], Subscript[m, 2]}, {Subscript[n, 3], Subscript[m, 3]}] /; Element[Subscript[n, 1], Integers] && Subscript[n, 1] >= 0 && Element[Subscript[n, 2], Integers] && Subscript[n, 2] >= 0 && Element[Subscript[n, 3], Integers] && Subscript[n, 3] >= 0 && Element[Subscript[m, 1], Integers] && Element[Subscript[m, 2], Integers] && Element[Subscript[m, 3], Integers] && Abs[Subscript[m, 1]] <= Subscript[n, 1] && Abs[Subscript[m, 2]] <= Subscript[n, 2] && Abs[Subscript[m, 3]] <= Subscript[n, 3]










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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