Spherical harmonic function: Specific values (formula 07.37.03.0037)

SphericalHarmonicY

$Mathematica Notation$

Hypergeometric Functions

SphericalHarmonicY[lambda,mu,theta,phi]

Specific values

Specialized values

For fixed mu,theta,phi

http://functions.wolfram.com/07.37.03.0037.01

Input Form

SphericalHarmonicY[10, \[Mu], \[CurlyTheta], \[CurlyPhi]] == (Sqrt[21] E^(I \[Mu] \[CurlyPhi]) (-893025 + 1057221 \[Mu]^2 - 172810 \[Mu]^4 + 8778 \[Mu]^6 - 165 \[Mu]^8 + \[Mu]^10 - 55 \[Mu] (251865 - 78877 \[Mu]^2 + 5754 \[Mu]^4 - 138 \[Mu]^6 + \[Mu]^8) Cos[\[CurlyTheta]] + 1485 (33075 - 29828 \[Mu]^2 + 3479 \[Mu]^4 - 112 \[Mu]^6 + \[Mu]^8) Cos[\[CurlyTheta]]^2 - 12870 \[Mu] (-16830 + 3773 \[Mu]^2 - 175 \[Mu]^4 + 2 \[Mu]^6) Cos[\[CurlyTheta]]^3 + 315315 (-1350 + 874 \[Mu]^2 - 65 \[Mu]^4 + \[Mu]^6) Cos[\[CurlyTheta]]^4 - 2837835 \[Mu] (314 - 45 \[Mu]^2 + \[Mu]^4) Cos[\[CurlyTheta]]^5 + 9459450 (135 - 56 \[Mu]^2 + 2 \[Mu]^4) Cos[\[CurlyTheta]]^6 - 45945900 \[Mu] (-29 + 2 \[Mu]^2) Cos[\[CurlyTheta]]^7 + 310134825 (-5 + \[Mu]^2) Cos[\[CurlyTheta]]^8 - 654729075 \[Mu] Cos[\[CurlyTheta]]^9 + 654729075 Cos[\[CurlyTheta]]^10) (Cos[\[CurlyTheta]/2]^2)^(\[Mu]/2))/(Sin[\[CurlyTheta]/2]^2)^(\[Mu]/2)/ (2 Sqrt[Pi] Sqrt[Gamma[11 - \[Mu]]] Sqrt[Gamma[11 + \[Mu]]])

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["SphericalHarmonicY", "[", RowBox[List["10", ",", "\[Mu]", ",", "\[CurlyTheta]", ",", "\[CurlyPhi]"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List[SqrtBox["21"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "\[Mu]", " ", "\[CurlyPhi]"]]], RowBox[List["(", RowBox[List[RowBox[List["-", "893025"]], "+", RowBox[List["1057221", " ", SuperscriptBox["\[Mu]", "2"]]], "-", RowBox[List["172810", " ", SuperscriptBox["\[Mu]", "4"]]], "+", RowBox[List["8778", " ", SuperscriptBox["\[Mu]", "6"]]], "-", RowBox[List["165", " ", SuperscriptBox["\[Mu]", "8"]]], "+", SuperscriptBox["\[Mu]", "10"], "-", RowBox[List["55", " ", "\[Mu]", " ", RowBox[List["(", RowBox[List["251865", "-", RowBox[List["78877", " ", SuperscriptBox["\[Mu]", "2"]]], "+", RowBox[List["5754", " ", SuperscriptBox["\[Mu]", "4"]]], "-", RowBox[List["138", " ", SuperscriptBox["\[Mu]", "6"]]], "+", SuperscriptBox["\[Mu]", "8"]]], ")"]], " ", RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]]]], "+", RowBox[List["1485", " ", RowBox[List["(", RowBox[List["33075", "-", RowBox[List["29828", " ", SuperscriptBox["\[Mu]", "2"]]], "+", RowBox[List["3479", " ", SuperscriptBox["\[Mu]", "4"]]], "-", RowBox[List["112", " ", SuperscriptBox["\[Mu]", "6"]]], "+", SuperscriptBox["\[Mu]", "8"]]], ")"]], " ", SuperscriptBox[RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]], "2"]]], "-", RowBox[List["12870", " ", "\[Mu]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "16830"]], "+", RowBox[List["3773", " ", SuperscriptBox["\[Mu]", "2"]]], "-", RowBox[List["175", " ", SuperscriptBox["\[Mu]", "4"]]], "+", RowBox[List["2", " ", SuperscriptBox["\[Mu]", "6"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]], "3"]]], "+", RowBox[List["315315", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1350"]], "+", RowBox[List["874", " ", SuperscriptBox["\[Mu]", "2"]]], "-", RowBox[List["65", " ", SuperscriptBox["\[Mu]", "4"]]], "+", SuperscriptBox["\[Mu]", "6"]]], ")"]], " ", SuperscriptBox[RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]], "4"]]], "-", RowBox[List["2837835", " ", "\[Mu]", " ", RowBox[List["(", RowBox[List["314", "-", RowBox[List["45", " ", SuperscriptBox["\[Mu]", "2"]]], "+", SuperscriptBox["\[Mu]", "4"]]], ")"]], " ", SuperscriptBox[RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]], "5"]]], "+", RowBox[List["9459450", " ", RowBox[List["(", RowBox[List["135", "-", RowBox[List["56", " ", SuperscriptBox["\[Mu]", "2"]]], "+", RowBox[List["2", " ", SuperscriptBox["\[Mu]", "4"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]], "6"]]], "-", RowBox[List["45945900", " ", "\[Mu]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "29"]], "+", RowBox[List["2", " ", SuperscriptBox["\[Mu]", "2"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]], "7"]]], "+", RowBox[List["310134825", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", SuperscriptBox["\[Mu]", "2"]]], ")"]], " ", SuperscriptBox[RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]], "8"]]], "-", RowBox[List["654729075", " ", "\[Mu]", " ", SuperscriptBox[RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]], "9"]]], "+", RowBox[List["654729075", " ", SuperscriptBox[RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]], "10"]]]]], ")"]], SuperscriptBox[RowBox[List["(", SuperscriptBox[RowBox[List["Cos", "[", FractionBox["\[CurlyTheta]", "2"], "]"]], "2"], ")"]], RowBox[List["\[Mu]", "/", "2"]]], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox[RowBox[List["Sin", "[", FractionBox["\[CurlyTheta]", "2"], "]"]], "2"], ")"]], RowBox[List[RowBox[List["-", "\[Mu]"]], "/", "2"]]]]], ")"]], "/", RowBox[List["(", RowBox[List["2", SqrtBox["\[Pi]"], SqrtBox[RowBox[List["Gamma", "[", RowBox[List["11", "-", "\[Mu]"]], "]"]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List["11", "+", "\[Mu]"]], "]"]]]]], ")"]]]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msubsup> <mi> Y </mi> <mn> 10 </mn> <mi> μ </mi> </msubsup> <mo> ( </mo> <mrow> <mi> ϑ </mi> <mo> , </mo> <mi> φ </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msqrt> <mn> 21 </mn> </msqrt> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> μ </mi> <mo> ⁢ </mo> <mi> φ </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 654729075 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> cos </mi> <mn> 10 </mn> </msup> <mo> ( </mo> <mi> ϑ </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 654729075 </mn> <mo> ⁢ </mo> <mi> μ </mi> <mo> ⁢ </mo> <mrow> <msup> <mi> cos </mi> <mn> 9 </mn> </msup> <mo> ( </mo> <mi> ϑ </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 310134825 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> μ </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> cos </mi> <mn> 8 </mn> </msup> <mo> ( </mo> <mi> ϑ </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 45945900 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mi> μ </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 29 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> μ </mi> <mo> ⁢ </mo> <mrow> <msup> <mi> cos </mi> <mn> 7 </mn> </msup> <mo> ( </mo> <mi> ϑ </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 9459450 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mi> μ </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 56 </mn> <mo> ⁢ </mo> <msup> <mi> μ </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 135 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> cos </mi> <mn> 6 </mn> </msup> <mo> ( </mo> <mi> ϑ </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2837835 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> μ </mi> <mn> 4 </mn> </msup> <mo> - </mo> <mrow> <mn> 45 </mn> <mo> ⁢ </mo> <msup> <mi> μ </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 314 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> μ </mi> <mo> ⁢ </mo> <mrow> <msup> <mi> cos </mi> <mn> 5 </mn> </msup> <mo> ( </mo> <mi> ϑ </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 315315 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> μ </mi> <mn> 6 </mn> </msup> <mo> - </mo> <mrow> <mn> 65 </mn> <mo> ⁢ </mo> <msup> <mi> μ </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 874 </mn> <mo> ⁢ </mo> <msup> <mi> μ </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 1350 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> cos </mi> <mn> 4 </mn> </msup> <mo> ( </mo> <mi> ϑ </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 12870 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mi> μ </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 175 </mn> <mo> ⁢ </mo> <msup> <mi> μ </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3773 </mn> <mo> ⁢ </mo> <msup> <mi> μ </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 16830 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> μ </mi> <mo> ⁢ </mo> <mtext> </mtext> <mrow> <msup> <mi> cos </mi> <mn> 3 </mn> </msup> <mo> ( </mo> <mi> ϑ </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 1485 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> μ </mi> <mn> 8 </mn> </msup> <mo> - </mo> <mrow> <mn> 112 </mn> <mo> ⁢ </mo> <msup> <mi> μ </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3479 </mn> <mo> ⁢ </mo> <msup> <mi> μ </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 29828 </mn> <mo> ⁢ </mo> <msup> <mi> μ </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 33075 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> cos </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> ϑ </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 55 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> μ </mi> <mn> 8 </mn> </msup> <mo> - </mo> <mrow> <mn> 138 </mn> <mo> ⁢ </mo> <msup> <mi> μ </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5754 </mn> <mo> ⁢ </mo> <msup> <mi> μ </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 78877 </mn> <mo> ⁢ </mo> <msup> <mi> μ </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 251865 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> μ </mi> <mo> ⁢ </mo> <mtext> </mtext> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> ϑ </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <msup> <mi> μ </mi> <mn> 10 </mn> </msup> <mo> - </mo> <mrow> <mn> 165 </mn> <mo> ⁢ </mo> <msup> <mi> μ </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 8778 </mn> <mo> ⁢ </mo> <msup> <mi> μ </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 172810 </mn> <mo> ⁢ </mo> <msup> <mi> μ </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1057221 </mn> <mo> ⁢ </mo> <msup> <mi> μ </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 893025 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <msup> <mi> cos </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mfrac> <mi> ϑ </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mrow> <mi> μ </mi> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <msup> <mi> sin </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mfrac> <mi> ϑ </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <mi> μ </mi> </mrow> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <msqrt> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> - </mo> <mi> μ </mi> </mrow> <mo> ) </mo> </mrow> </msqrt> <mo> ⁢ </mo> <msqrt> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> μ </mi> <mo> + </mo> <mn> 11 </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'> 10 </cn> <ci> μ </ci> <ci> ϑ </ci> <ci> φ </ci> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> 21 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <ci> μ </ci> <ci> φ </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 654729075 </cn> <apply> <power /> <apply> <cos /> <ci> ϑ </ci> </apply> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 654729075 </cn> <ci> μ </ci> <apply> <power /> <apply> <cos /> <ci> ϑ </ci> </apply> <cn type='integer'> 9 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 310134825 </cn> <apply> <plus /> <apply> <power /> <ci> μ </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -5 </cn> </apply> <apply> <power /> <apply> <cos /> <ci> ϑ </ci> </apply> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 45945900 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> μ </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -29 </cn> </apply> <ci> μ </ci> <apply> <power /> <apply> <cos /> <ci> ϑ </ci> </apply> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 9459450 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> μ </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 56 </cn> <apply> <power /> <ci> μ </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 135 </cn> </apply> <apply> <power /> <apply> <cos /> <ci> ϑ </ci> </apply> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2837835 </cn> <apply> <plus /> <apply> <power /> <ci> μ </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 45 </cn> <apply> <power /> <ci> μ </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 314 </cn> </apply> <ci> μ </ci> <apply> <power /> <apply> <cos /> <ci> ϑ </ci> </apply> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 315315 </cn> <apply> <plus /> <apply> <power /> <ci> μ </ci> <cn type='integer'> 6 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 65 </cn> <apply> <power /> <ci> μ </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 874 </cn> <apply> <power /> <ci> μ </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1350 </cn> </apply> <apply> <power /> <apply> <cos /> <ci> ϑ </ci> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 12870 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> μ </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 175 </cn> <apply> <power /> <ci> μ </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3773 </cn> <apply> <power /> <ci> μ </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -16830 </cn> </apply> <ci> μ </ci> <apply> <power /> <apply> <cos /> <ci> ϑ </ci> </apply> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1485 </cn> <apply> <plus /> <apply> <power /> <ci> μ </ci> <cn type='integer'> 8 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 112 </cn> <apply> <power /> <ci> μ </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3479 </cn> <apply> <power /> <ci> μ </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 29828 </cn> <apply> <power /> <ci> μ </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 33075 </cn> </apply> <apply> <power /> <apply> <cos /> <ci> ϑ </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 55 </cn> <apply> <plus /> <apply> <power /> <ci> μ </ci> <cn type='integer'> 8 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 138 </cn> <apply> <power /> <ci> μ </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5754 </cn> <apply> <power /> <ci> μ </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 78877 </cn> <apply> <power /> <ci> μ </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 251865 </cn> </apply> <ci> μ </ci> <apply> <cos /> <ci> ϑ </ci> </apply> </apply> </apply> <apply> <power /> <ci> μ </ci> <cn type='integer'> 10 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 165 </cn> <apply> <power /> <ci> μ </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 8778 </cn> <apply> <power /> <ci> μ </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 172810 </cn> <apply> <power /> <ci> μ </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1057221 </cn> <apply> <power /> <ci> μ </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -893025 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <cos /> <apply> <times /> <ci> ϑ </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> μ </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> ϑ </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> μ </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'> 11 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> μ </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> μ </ci> <cn type='integer'> 11 </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

SphericalHarmonicY[n,m,theta,phi]