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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/07.37.03.0034.01









  


  










Input Form





SphericalHarmonicY[7, \[Mu], \[CurlyTheta], \[CurlyPhi]] == (Sqrt[15] E^(I \[Mu] \[CurlyPhi]) ((-\[Mu]) (-2304 + 784 \[Mu]^2 - 56 \[Mu]^4 + \[Mu]^6) + 7 (-1575 + 1516 \[Mu]^2 - 170 \[Mu]^4 + 4 \[Mu]^6) Cos[\[CurlyTheta]] - 189 \[Mu] (283 - 60 \[Mu]^2 + 2 \[Mu]^4) Cos[\[CurlyTheta]]^2 + 1575 (63 - 38 \[Mu]^2 + 2 \[Mu]^4) Cos[\[CurlyTheta]]^3 - 17325 \[Mu] (-10 + \[Mu]^2) Cos[\[CurlyTheta]]^4 + 31185 (-7 + 2 \[Mu]^2) Cos[\[CurlyTheta]]^5 - 135135 \[Mu] Cos[\[CurlyTheta]]^6 + 135135 Cos[\[CurlyTheta]]^7) (Cos[\[CurlyTheta]/2]^2)^(\[Mu]/2))/(Sin[\[CurlyTheta]/2]^2)^(\[Mu]/2)/ (2 Sqrt[Pi] Sqrt[Gamma[8 - \[Mu]]] Sqrt[Gamma[8 + \[Mu]]])










Standard Form





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MathML Form







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</mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#977; </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> &#956; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#956; </mi> <mn> 6 </mn> </msup> <mo> - </mo> <mrow> <mn> 56 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 784 </mn> <mo> &#8290; </mo> <msup> <mi> &#956; </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 2304 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <msup> <mi> cos </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mfrac> <mi> &#977; </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mrow> <mi> &#956; </mi> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <msup> <mi> sin </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mfrac> <mi> &#977; </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <mi> &#956; </mi> </mrow> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 8 </mn> <mo> - </mo> <mi> &#956; </mi> </mrow> <mo> ) </mo> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#956; </mi> <mo> + </mo> <mn> 8 </mn> </mrow> <mo> ) </mo> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> SphericalHarmonicY </ci> <cn type='integer'> 7 </cn> <ci> &#956; </ci> <ci> &#977; </ci> <ci> &#966; </ci> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> 15 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <ci> &#956; </ci> <ci> &#966; </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 135135 </cn> <apply> <power /> <apply> <cos /> <ci> &#977; </ci> </apply> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 135135 </cn> <ci> &#956; 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</ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 63 </cn> </apply> <apply> <power /> <apply> <cos /> <ci> &#977; </ci> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 189 </cn> <ci> &#956; </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> &#956; </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 60 </cn> <apply> <power /> <ci> &#956; </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 283 </cn> </apply> <apply> <power /> <apply> <cos /> <ci> &#977; </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 7 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> &#956; </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 170 </cn> <apply> <power /> <ci> &#956; 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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'> 8 </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'> 8 </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





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