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http://functions.wolfram.com/05.09.17.0006.01
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n (n + 2 \[Lambda]) GegenbauerC[n, \[Lambda], z] -
2 z \[Lambda] (1 + 2 \[Lambda]) GegenbauerC[n - 1, 1 + \[Lambda], z] -
4 (z^2 - 1) \[Lambda] (1 + \[Lambda]) GegenbauerC[n - 2, 2 + \[Lambda],
z] == 0
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["n", " ", RowBox[List["(", RowBox[List["n", "+", RowBox[List["2", " ", "\[Lambda]"]]]], ")"]], " ", RowBox[List["GegenbauerC", "[", RowBox[List["n", ",", "\[Lambda]", ",", "z"]], "]"]]]], "-", RowBox[List["2", " ", "z", " ", "\[Lambda]", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Lambda]"]]]], ")"]], " ", RowBox[List["GegenbauerC", "[", RowBox[List[RowBox[List["n", "-", "1"]], ",", RowBox[List["1", "+", "\[Lambda]"]], ",", "z"]], "]"]]]], "-", RowBox[List["4", " ", RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "-", "1"]], ")"]], " ", "\[Lambda]", " ", RowBox[List["(", RowBox[List["1", "+", "\[Lambda]"]], ")"]], " ", RowBox[List["GegenbauerC", "[", RowBox[List[RowBox[List["n", "-", "2"]], ",", RowBox[List["2", "+", "\[Lambda]"]], ",", "z"]], "]"]]]]]], "\[Equal]", "0"]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> λ </mi> </mrow> <mo> + </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> n </mi> <mo> ⁢ </mo> <mrow> <msubsup> <mi> C </mi> <mi> n </mi> <mi> λ </mi> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mi> λ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> λ </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msubsup> <mi> C </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mi> λ </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> λ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> λ </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msubsup> <mi> C </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mrow> <mi> λ </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mn> 0 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> λ </ci> </apply> <ci> n </ci> </apply> <ci> n </ci> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> C </ci> <ci> n </ci> </apply> <ci> λ </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <ci> λ </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> λ </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> C </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <ci> λ </ci> <cn type='integer'> 1 </cn> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <ci> λ </ci> <apply> <plus /> <ci> λ </ci> <cn type='integer'> 1 </cn> </apply> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> C </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -2 </cn> </apply> </apply> <apply> <plus /> <ci> λ </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["n_", " ", RowBox[List["(", RowBox[List["n_", "+", RowBox[List["2", " ", "\[Lambda]_"]]]], ")"]], " ", RowBox[List["GegenbauerC", "[", RowBox[List["n_", ",", "\[Lambda]_", ",", "z_"]], "]"]]]], "-", RowBox[List["2", " ", "z_", " ", "\[Lambda]_", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Lambda]_"]]]], ")"]], " ", RowBox[List["GegenbauerC", "[", RowBox[List[RowBox[List["n_", "-", "1"]], ",", RowBox[List["1", "+", "\[Lambda]_"]], ",", "z_"]], "]"]]]], "-", RowBox[List["4", " ", RowBox[List["(", RowBox[List[SuperscriptBox["z_", "2"], "-", "1"]], ")"]], " ", "\[Lambda]_", " ", RowBox[List["(", RowBox[List["1", "+", "\[Lambda]_"]], ")"]], " ", RowBox[List["GegenbauerC", "[", RowBox[List[RowBox[List["n_", "-", "2"]], ",", RowBox[List["2", "+", "\[Lambda]_"]], ",", "z_"]], "]"]]]]]], "]"]], "\[RuleDelayed]", "0"]]]] |
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Date Added to functions.wolfram.com (modification date)
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