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variants of this functions
GegenbauerC




Mathematica Notation

Traditional Notation









Hypergeometric Functions > GegenbauerC[nu,z] > Transformations > Related transformations





http://functions.wolfram.com/07.13.16.0004.01









  


  








Input Form





GegenbauerC[n, (m/2) GegenbauerC[m, z]] == m GegenbauerC[n m, z] /; Element[m, Integers] && m > 0 && Element[n, Integers] && n > 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["GegenbauerC", "[", RowBox[List["n", ",", RowBox[List[FractionBox["m", "2"], RowBox[List["GegenbauerC", "[", RowBox[List["m", ",", "z"]], "]"]]]]]], "]"]], "\[Equal]", RowBox[List["m", " ", RowBox[List["GegenbauerC", "[", RowBox[List[RowBox[List["n", " ", "m"]], ",", "z"]], "]"]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]], "\[And]", RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", ">", "0"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msubsup> <mi> C </mi> <mi> n </mi> <mrow> <mo> ( </mo> <mn> 0 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mrow> <mfrac> <mi> m </mi> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <msubsup> <mi> C </mi> <mi> m </mi> <mrow> <mo> ( </mo> <mn> 0 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mrow> <msubsup> <mi> C </mi> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> <mrow> <mo> ( </mo> <mn> 0 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> m </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> <mo> &#8743; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> GegenbauerC </ci> <ci> n </ci> <cn type='integer'> 0 </cn> <apply> <times /> <apply> <times /> <ci> m </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> GegenbauerC </ci> <ci> m </ci> <cn type='integer'> 0 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <ci> m </ci> <apply> <ci> GegenbauerC </ci> <apply> <times /> <ci> m </ci> <ci> n </ci> </apply> <cn type='integer'> 0 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> m </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> <apply> <in /> <ci> n </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["GegenbauerC", "[", RowBox[List["n_", ",", RowBox[List[FractionBox["1", "2"], " ", "m_", " ", RowBox[List["GegenbauerC", "[", RowBox[List["m_", ",", "z_"]], "]"]]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["m", " ", RowBox[List["GegenbauerC", "[", RowBox[List[RowBox[List["n", " ", "m"]], ",", "z"]], "]"]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "&&", RowBox[List["m", ">", "0"]], "&&", RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]]]]]]]]]]


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





2001-10-29