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variants of this functions
ChebyshevT




Mathematica Notation

Traditional Notation









Polynomials > ChebyshevT[n,z] > Representations through equivalent functions > With related functions





http://functions.wolfram.com/05.04.27.0004.01









  


  








Input Form





ChebyshevT[n, z] == (1/n) (D[(z^2 - 1) ChebyshevU[n - 1, z], z] - z ChebyshevU[n - 1, z])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["ChebyshevT", "[", RowBox[List["n", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "n"], RowBox[List["(", RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "z"], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "-", "1"]], ")"]], " ", RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["n", "-", "1"]], ",", "z"]], "]"]]]], ")"]]]], "-", RowBox[List["z", " ", RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["n", "-", "1"]], ",", "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> <msub> <mi> T </mi> <mi> n </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mi> n </mi> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> U </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> z </mi> </mrow> </mfrac> <mo> - </mo> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <msub> <mi> U </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> ChebyshevT </ci> <ci> n </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <ci> ChebyshevU </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> z </ci> <apply> <ci> ChebyshevU </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ChebyshevT", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z"]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "-", "1"]], ")"]], " ", RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["n", "-", "1"]], ",", "z"]], "]"]]]], ")"]]]], "-", RowBox[List["z", " ", RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["n", "-", "1"]], ",", "z"]], "]"]]]]]], "n"]]]]]


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





2001-10-29