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variants of this functions
SphericalHarmonicY




Mathematica Notation

Traditional Notation









Polynomials > SphericalHarmonicY[n,m,theta,phi] > Specific values > Specialized values > For fixed m, theta, phi





http://functions.wolfram.com/05.10.03.0024.01









  


  








Input Form





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








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> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </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> m </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> m </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