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variants of this functions
SphericalHarmonicY






Mathematica Notation

Traditional Notation









Hypergeometric Functions > SphericalHarmonicY[lambda,mu,theta,phi] > Representations through more general functions > Through hypergeometric functions > Involving 2F1





http://functions.wolfram.com/07.37.26.0003.01









  


  










Input Form





SphericalHarmonicY[\[Lambda], \[Mu], \[CurlyTheta], \[CurlyPhi]] == Sqrt[(2 \[Lambda] + 1)/(4 Pi)] (Sqrt[Gamma[\[Lambda] - \[Mu] + 1]]/ Sqrt[Gamma[\[Lambda] + \[Mu] + 1]]) E^(I \[CurlyPhi] \[Mu]) ((Gamma[-\[Mu]]/(Gamma[-\[Lambda] - \[Mu]] Gamma[\[Lambda] - \[Mu] + 1])) ((Cos[\[CurlyTheta]/2]^2)^(\[Mu]/2)/(Sin[\[CurlyTheta]/2]^2)^(\[Mu]/2)) Hypergeometric2F1[-\[Lambda], \[Lambda] + 1, 1 + \[Mu], Cos[\[CurlyTheta]/2]^2] - ((Sin[Pi \[Lambda]] Gamma[\[Mu]])/Pi) (1/((Cos[\[CurlyTheta]/2]^2)^(\[Mu]/2) (Sin[\[CurlyTheta]/2]^2)^ (\[Mu]/2))) Hypergeometric2F1[\[Lambda] - \[Mu] + 1, -\[Lambda] - \[Mu], 1 - \[Mu], Cos[\[CurlyTheta]/2]^2]) /; !Element[\[Mu], Integers]










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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