Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

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
GegenbauerC






Mathematica Notation

Traditional Notation









Polynomials > GegenbauerC[n,lambda,z] > Specific values > Specialized values > For fixed lambda, z





http://functions.wolfram.com/05.09.03.0016.01









  


  










Input Form





GegenbauerC[6, \[Lambda], z] == (4/45) \[Lambda] (\[Lambda] + 1) (\[Lambda] + 2) (\[Lambda] + 3) (\[Lambda] + 4) (\[Lambda] + 5) z^6 - (2/3) \[Lambda] (\[Lambda] + 1) (\[Lambda] + 2) (\[Lambda] + 3) (\[Lambda] + 4) z^4 + \[Lambda] (\[Lambda] + 1) (\[Lambda] + 2) (\[Lambda] + 3) z^2 - (1/6) \[Lambda] (\[Lambda] + 1) (\[Lambda] + 2)










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["GegenbauerC", "[", RowBox[List["6", ",", "\[Lambda]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["4", "45"], " ", "\[Lambda]", " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "4"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "5"]], ")"]], " ", SuperscriptBox["z", "6"]]], "-", RowBox[List[FractionBox["2", "3"], " ", "\[Lambda]", " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "4"]], ")"]], " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["\[Lambda]", " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "3"]], ")"]], " ", SuperscriptBox["z", "2"]]], "-", RowBox[List[FractionBox["1", "6"], " ", "\[Lambda]", " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "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> C </mi> <mn> 6 </mn> <mi> &#955; </mi> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mfrac> <mn> 4 </mn> <mn> 45 </mn> </mfrac> <mo> &#8290; </mo> <mi> &#955; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#955; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#955; </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#955; </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#955; </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#955; </mi> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> <mo> &#8290; </mo> <mi> &#955; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#955; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#955; </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#955; </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#955; </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> &#955; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#955; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#955; </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#955; </mi> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 6 </mn> </mfrac> <mo> &#8290; </mo> <mi> &#955; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#955; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#955; </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> C </ci> <cn type='integer'> 6 </cn> </apply> <ci> &#955; </ci> </apply> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 4 <sep /> 45 </cn> <ci> &#955; </ci> <apply> <plus /> <ci> &#955; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> &#955; </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> &#955; </ci> <cn type='integer'> 4 </cn> </apply> <apply> <plus /> <ci> &#955; </ci> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 2 <sep /> 3 </cn> <ci> &#955; </ci> <apply> <plus /> <ci> &#955; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> &#955; </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> &#955; </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <ci> &#955; </ci> <apply> <plus /> <ci> &#955; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> &#955; </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 6 </cn> <ci> &#955; </ci> <apply> <plus /> <ci> &#955; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["GegenbauerC", "[", RowBox[List["6", ",", "\[Lambda]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["4", "45"], " ", "\[Lambda]", " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "4"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "5"]], ")"]], " ", SuperscriptBox["z", "6"]]], "-", RowBox[List[FractionBox["2", "3"], " ", "\[Lambda]", " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "3"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "4"]], ")"]], " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["\[Lambda]", " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "2"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "3"]], ")"]], " ", SuperscriptBox["z", "2"]]], "-", RowBox[List[FractionBox["1", "6"], " ", "\[Lambda]", " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Lambda]", "+", "2"]], ")"]]]]]]]]]]










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





2001-10-29





© 1998-2014 Wolfram Research, Inc.