Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











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/05.10.03.0036.01









  


  








Input Form





SphericalHarmonicY[2, -1, \[CurlyTheta], \[CurlyPhi]] == ((1/2) Sqrt[15/(2 Pi)] Cos[\[CurlyTheta]] Sqrt[Sin[\[CurlyTheta]]^2])/ E^(I \[CurlyPhi])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["SphericalHarmonicY", "[", RowBox[List["2", ",", RowBox[List["-", "1"]], ",", "\[CurlyTheta]", ",", "\[CurlyPhi]"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "\[CurlyPhi]"]]], " ", SqrtBox[FractionBox["15", RowBox[List["2", " ", "\[Pi]"]]]], " ", RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]], " ", SqrtBox[SuperscriptBox[RowBox[List["Sin", "[", "\[CurlyTheta]", "]"]], "2"]]]]]]]]








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> 2 </mn> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> ( </mo> <mrow> <mi> &#977; </mi> <mo> , </mo> <mi> &#966; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <mi> &#966; </mi> </mrow> </msup> <mo> &#8290; </mo> <msqrt> <mfrac> <mn> 15 </mn> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> </msqrt> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#977; </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mrow> <msup> <mi> sin </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> &#977; </mi> <mo> ) </mo> </mrow> </msqrt> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> SphericalHarmonicY </ci> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> <ci> &#977; </ci> <ci> &#966; </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> &#966; </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <cos /> <ci> &#977; </ci> </apply> <apply> <power /> <apply> <power /> <apply> <sin /> <ci> &#977; </ci> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["SphericalHarmonicY", "[", RowBox[List["2", ",", RowBox[List["-", "1"]], ",", "\[CurlyTheta]_", ",", "\[CurlyPhi]_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "\[CurlyPhi]"]]], " ", SqrtBox[FractionBox["15", RowBox[List["2", " ", "\[Pi]"]]]], " ", RowBox[List["Cos", "[", "\[CurlyTheta]", "]"]], " ", SqrtBox[SuperscriptBox[RowBox[List["Sin", "[", "\[CurlyTheta]", "]"]], "2"]]]]]]]]


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





2001-10-29