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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/07.37.03.0036.01









  


  










Input Form





SphericalHarmonicY[9, \[Mu], \[CurlyTheta], \[CurlyPhi]] == (Sqrt[19] E^(I \[Mu] \[CurlyPhi]) ((-\[Mu]) (147456 - 52480 \[Mu]^2 + 4368 \[Mu]^4 - 120 \[Mu]^6 + \[Mu]^8) + 45 (19845 - 20217 \[Mu]^2 + 2674 \[Mu]^4 - 98 \[Mu]^6 + \[Mu]^8) Cos[\[CurlyTheta]] - 495 \[Mu] (-11601 + 2933 \[Mu]^2 - 154 \[Mu]^4 + 2 \[Mu]^6) Cos[\[CurlyTheta]]^2 + 6930 (-1890 + 1373 \[Mu]^2 - 115 \[Mu]^4 + 2 \[Mu]^6) Cos[\[CurlyTheta]]^3 - 135135 \[Mu] (249 - 40 \[Mu]^2 + \[Mu]^4) Cos[\[CurlyTheta]]^4 + 945945 (54 - 25 \[Mu]^2 + \[Mu]^4) Cos[\[CurlyTheta]]^5 - 4729725 \[Mu] (-13 + \[Mu]^2) Cos[\[CurlyTheta]]^6 + 8108100 (-9 + 2 \[Mu]^2) Cos[\[CurlyTheta]]^7 - 34459425 \[Mu] Cos[\[CurlyTheta]]^8 + 34459425 Cos[\[CurlyTheta]]^9) (Cos[\[CurlyTheta]/2]^2)^(\[Mu]/2))/(Sin[\[CurlyTheta]/2]^2)^(\[Mu]/2)/ (2 Sqrt[Pi] Sqrt[Gamma[10 - \[Mu]]] Sqrt[Gamma[10 + \[Mu]]])










Standard Form





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MathML Form







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</ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <sin /> <apply> <times /> <ci> &#977; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#956; </ci> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <cn type='integer'> 10 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#956; </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> &#956; </ci> <cn type='integer'> 10 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29