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variants of this functions
GegenbauerC




Mathematica Notation

Traditional Notation









Hypergeometric Functions > GegenbauerC[nu,z] > Identities > Functional identities > Relations between contiguous functions





http://functions.wolfram.com/07.13.17.0007.01









  


  








Input Form





GegenbauerC[\[Nu], z] == ((2 (\[Nu] + 1) z)/\[Nu]) GegenbauerC[\[Nu] + 1, z] - ((\[Nu] + 2)/\[Nu]) GegenbauerC[\[Nu] + 2, z]








Standard Form





Cell[BoxData[RowBox[List[" ", RowBox[List[RowBox[List["GegenbauerC", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["\[Nu]", "+", "1"]], ")"]], " ", "z"]], "\[Nu]"], " ", RowBox[List["GegenbauerC", "[", RowBox[List[RowBox[List["\[Nu]", "+", "1"]], ",", "z"]], "]"]]]], "-", RowBox[List[FractionBox[RowBox[List["\[Nu]", "+", "2"]], "\[Nu]"], " ", RowBox[List["GegenbauerC", "[", RowBox[List[RowBox[List["\[Nu]", "+", "2"]], ",", "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> &#63449; </mo> <mrow> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mi> &#957; </mi> </mfrac> <mo> &#8290; </mo> <mrow> <msubsup> <mi> C </mi> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 0 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mi> &#957; </mi> </mfrac> <mo> &#8290; </mo> <mrow> <msubsup> <mi> C </mi> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mrow> <mo> ( </mo> <mn> 0 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </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> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <ci> z </ci> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> GegenbauerC </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 0 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> GegenbauerC </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 0 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["GegenbauerC", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["2", " ", RowBox[List["(", RowBox[List["\[Nu]", "+", "1"]], ")"]], " ", "z"]], ")"]], " ", RowBox[List["GegenbauerC", "[", RowBox[List[RowBox[List["\[Nu]", "+", "1"]], ",", "z"]], "]"]]]], "\[Nu]"], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["\[Nu]", "+", "2"]], ")"]], " ", RowBox[List["GegenbauerC", "[", RowBox[List[RowBox[List["\[Nu]", "+", "2"]], ",", "z"]], "]"]]]], "\[Nu]"]]]]]]]


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





2007-05-02