SphericalHarmonicY[n, m, \[CurlyTheta], \[CurlyPhi]] == Sqrt[(2 n + 1)/(4 Pi)] WignerD[n, 0, -m, 0, \[CurlyTheta], \[CurlyPhi]]

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<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> <mi> n </mi> <mi> m </mi> </msubsup> <mo> ( </mo> <mrow> <mi> &#977; </mi> <mo> , </mo> <mi> &#966; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msqrt> <mfrac> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> n </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> </msqrt> <mo> &#8290; </mo> <mrow> <msubsup> <mi> D </mi> <mrow> <mn> 0 </mn> <mo> , </mo> <mrow> <mo> - </mo> <mi> m </mi> </mrow> </mrow> <mi> n </mi> </msubsup> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mi> &#977; </mi> <mo> , </mo> <mi> &#966; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> SphericalHarmonicY </ci> <ci> n </ci> <ci> m </ci> <ci> &#977; </ci> <ci> &#966; </ci> </apply> <apply> <times /> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> D </ci> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> <ci> n </ci> </apply> <cn type='integer'> 0 </cn> <ci> &#977; </ci> <ci> &#966; </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["SphericalHarmonicY", "[", RowBox[List["n_", ",", "m_", ",", "\[CurlyTheta]_", ",", "\[CurlyPhi]_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SqrtBox[FractionBox[RowBox[List[RowBox[List["2", " ", "n"]], "+", "1"]], RowBox[List["4", " ", "\[Pi]"]]]], " ", RowBox[List["WignerD", "[", RowBox[List["n", ",", "0", ",", RowBox[List["-", "m"]], ",", "0", ",", "\[CurlyTheta]", ",", "\[CurlyPhi]"]], "]"]]]]]]]]

2001-10-29