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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 n, phi





http://functions.wolfram.com/05.10.03.0051.01









  


  








Input Form





SphericalHarmonicY[4, 0, \[CurlyTheta], \[CurlyPhi]] == (3/(16 Sqrt[Pi])) (3 - 30 Cos[\[CurlyTheta]]^2 + 35 Cos[\[CurlyTheta]]^4)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["SphericalHarmonicY", "[", RowBox[List["4", ",", "0", ",", "\[CurlyTheta]", ",", "\[CurlyPhi]"]], "]"]], "\[Equal]", RowBox[List[FractionBox["3", RowBox[List["16", " ", SqrtBox["\[Pi]"]]]], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["30", " ", SuperscriptBox[RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]], "2"]]], "+", RowBox[List["35", " ", SuperscriptBox[RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]], "4"]]]]], ")"]]]]]]]]








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> 4 </mn> <mn> 0 </mn> </msubsup> <mo> ( </mo> <mrow> <mi> &#977; </mi> <mo> , </mo> <mi> &#966; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 3 </mn> <mrow> <mn> 16 </mn> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 35 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> cos </mi> <mn> 4 </mn> </msup> <mo> ( </mo> <mi> &#977; </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 30 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> cos </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> &#977; </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> SphericalHarmonicY </ci> <cn type='integer'> 4 </cn> <cn type='integer'> 0 </cn> <ci> &#977; </ci> <ci> &#966; </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 35 </cn> <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'> 30 </cn> <apply> <power /> <apply> <cos /> <ci> &#977; </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["SphericalHarmonicY", "[", RowBox[List["4", ",", "0", ",", "\[CurlyTheta]_", ",", "\[CurlyPhi]_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["3", " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["30", " ", SuperscriptBox[RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]], "2"]]], "+", RowBox[List["35", " ", SuperscriptBox[RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]], "4"]]]]], ")"]]]], RowBox[List["16", " ", SqrtBox["\[Pi]"]]]]]]]]


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





2001-10-29