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variants of this functions
SphericalHarmonicY






Mathematica Notation

Traditional Notation









Hypergeometric Functions > SphericalHarmonicY[lambda,mu,theta,phi] > Specific values > Specialized values > For fixed mu,theta,phi





http://functions.wolfram.com/07.37.03.0035.01









  


  










Input Form





SphericalHarmonicY[8, \[Mu], \[CurlyTheta], \[CurlyPhi]] == (Sqrt[17] E^(I \[Mu] \[CurlyPhi]) (11025 - 12916 \[Mu]^2 + 1974 \[Mu]^4 - 84 \[Mu]^6 + \[Mu]^8 - 9 \[Mu] (-15159 + 4396 \[Mu]^2 - 266 \[Mu]^4 + 4 \[Mu]^6) Cos[\[CurlyTheta]] + 315 (-1260 + 1043 \[Mu]^2 - 100 \[Mu]^4 + 2 \[Mu]^6) Cos[\[CurlyTheta]]^2 - 3465 \[Mu] (383 - 70 \[Mu]^2 + 2 \[Mu]^4) Cos[\[CurlyTheta]]^3 + 51975 (42 - 22 \[Mu]^2 + \[Mu]^4) Cos[\[CurlyTheta]]^4 - 135135 \[Mu] (-23 + 2 \[Mu]^2) Cos[\[CurlyTheta]]^5 + 945945 (-4 + \[Mu]^2) Cos[\[CurlyTheta]]^6 - 2027025 \[Mu] Cos[\[CurlyTheta]]^7 + 2027025 Cos[\[CurlyTheta]]^8) (Cos[\[CurlyTheta]/2]^2)^(\[Mu]/2))/(Sin[\[CurlyTheta]/2]^2)^(\[Mu]/2)/ (2 Sqrt[Pi] Sqrt[Gamma[9 - \[Mu]]] Sqrt[Gamma[9 + \[Mu]]])










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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