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http://functions.wolfram.com/05.10.03.0052.01
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SphericalHarmonicY[4, 1, \[CurlyTheta], \[CurlyPhi]] ==
(-(3/8)) Sqrt[5/Pi] E^(I \[CurlyPhi]) Cos[\[CurlyTheta]]
(-3 + 7 Cos[\[CurlyTheta]]^2) Sqrt[Sin[\[CurlyTheta]]^2]
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Cell[BoxData[RowBox[List[RowBox[List["SphericalHarmonicY", "[", RowBox[List["4", ",", "1", ",", "\[CurlyTheta]", ",", "\[CurlyPhi]"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["3", "8"]]], " ", SqrtBox[FractionBox["5", "\[Pi]"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "\[CurlyPhi]"]]], " ", RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["7", " ", SuperscriptBox[RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]], "2"]]]]], ")"]], " ", SqrtBox[SuperscriptBox[RowBox[List["Sin", "[", "\[CurlyTheta]", "]"]], "2"]]]]]]]]
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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> <mn> 4 </mn> <mn> 1 </mn> </msubsup> <mo> ( </mo> <mrow> <mi> ϑ </mi> <mo> , </mo> <mi> φ </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 3 </mn> <mn> 8 </mn> </mfrac> </mrow> <mo> ⁢ </mo> <msqrt> <mfrac> <mn> 5 </mn> <mi> π </mi> </mfrac> </msqrt> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> φ </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> ϑ </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mrow> <msup> <mi> cos </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> ϑ </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mrow> <msup> <mi> sin </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> ϑ </mi> <mo> ) </mo> </mrow> </msqrt> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> SphericalHarmonicY </ci> <cn type='integer'> 4 </cn> <cn type='integer'> 1 </cn> <ci> ϑ </ci> <ci> φ </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 8 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <ci> φ </ci> </apply> </apply> <apply> <cos /> <ci> ϑ </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 7 </cn> <apply> <power /> <apply> <cos /> <ci> ϑ </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <sin /> <ci> ϑ </ci> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["SphericalHarmonicY", "[", RowBox[List["4", ",", "1", ",", "\[CurlyTheta]_", ",", "\[CurlyPhi]_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["-", "3"]], ")"]], " ", SqrtBox[FractionBox["5", "\[Pi]"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "\[CurlyPhi]"]]], " ", RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["7", " ", SuperscriptBox[RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]], "2"]]]]], ")"]], " ", SqrtBox[SuperscriptBox[RowBox[List["Sin", "[", "\[CurlyTheta]", "]"]], "2"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
