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variants of this functions
GegenbauerC




Mathematica Notation

Traditional Notation









Hypergeometric Functions > GegenbauerC[nu,z] > Primary definition





http://functions.wolfram.com/07.13.02.0001.01









  


  








Input Form





GegenbauerC[\[Nu], z] == (2/\[Nu]) ChebyshevT[\[Nu], z] == (2/\[Nu]) Cos[\[Nu] ArcCos[z]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["GegenbauerC", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["2", "\[Nu]"], RowBox[List["ChebyshevT", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["2", " "]], RowBox[List["\[Nu]", " "]]], RowBox[List["Cos", "[", RowBox[List["\[Nu]", " ", RowBox[List["ArcCos", "[", "z", "]"]]]], "]"]]]]]]]]








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> C </mi> <mi> &#957; </mi> <mrow> <mo> ( </mo> <mn> 0 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 2 </mn> <mi> &#957; </mi> </mfrac> <mo> &#8290; </mo> <mrow> <msub> <mi> T </mi> <mi> &#957; </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> cos </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mi> &#957; </mi> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> GegenbauerC </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> ChebyshevT </ci> <ci> &#957; </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <cos /> <apply> <times /> <ci> &#957; </ci> <apply> <arccos /> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["GegenbauerC", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", FractionBox[RowBox[List["2", " ", RowBox[List["ChebyshevT", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]], "\[Nu]"], "\[Equal]", FractionBox[RowBox[List["2", " ", RowBox[List["Cos", "[", RowBox[List["\[Nu]", " ", RowBox[List["ArcCos", "[", "z", "]"]]]], "]"]]]], "\[Nu]"]]]]]


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





2001-10-29