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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/05.10.03.0023.01









  


  








Input Form





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








Standard Form





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MathML Form







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</ci> </apply> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 51975 </cn> <apply> <plus /> <apply> <power /> <ci> m </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 22 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 42 </cn> </apply> <apply> <power /> <apply> <cos /> <ci> &#977; </ci> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3465 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 70 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 383 </cn> </apply> <ci> m </ci> <apply> <power /> <apply> <cos /> <ci> &#977; 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</ci> </apply> </apply> </apply> <apply> <power /> <ci> m </ci> <cn type='integer'> 8 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 84 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1974 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 12916 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 11025 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <cos /> <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 /> <ci> m </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; 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Rule Form





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





2001-10-29