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variants of this functions
ChebyshevT




Mathematica Notation

Traditional Notation









Polynomials > ChebyshevT[n,z] > Generating functions





http://functions.wolfram.com/05.04.11.0001.01









  


  








Input Form





ChebyshevT[n, z] == SeriesTerm[(1 - t z)/(t^2 - 2 t z + 1), {t, 0, n}] /; -1 < z < 1








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ChebyshevT", "[", RowBox[List["n", ",", "z"]], "]"]], "\[Equal]", RowBox[List["SeriesTerm", "[", RowBox[List[FractionBox[RowBox[List["1", "-", RowBox[List["t", " ", "z"]]]], RowBox[List[SuperscriptBox["t", "2"], "-", RowBox[List["2", " ", "t", " ", "z"]], "+", "1"]]], ",", RowBox[List["{", RowBox[List["t", ",", "0", ",", "n"]], "}"]]]], "]"]]]], "/;", RowBox[List[RowBox[List["-", "1"]], "<", "z", "<", "1"]]]]]]








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> <msub> <mi> T </mi> <mi> n </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> [ </mo> <msup> <mi> t </mi> <mi> n </mi> </msup> <mtext> </mtext> <mo> ] </mo> </mrow> <mo> &#8290; </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mi> t </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mrow> <msup> <mi> t </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mi> t </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> &lt; </mo> <mi> z </mi> <mo> &lt; </mo> <mn> 1 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <msub> <mi> T </mi> <mi> n </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> [ </mo> <msup> <mi> t </mi> <mi> n </mi> </msup> <mtext> </mtext> <mo> ] </mo> </mrow> <mo> &#8290; </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mi> t </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mrow> <msup> <mi> t </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mi> t </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> &lt; </mo> <mi> z </mi> <mo> &lt; </mo> <mn> 1 </mn> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ChebyshevT", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["SeriesTerm", "[", RowBox[List[FractionBox[RowBox[List["1", "-", RowBox[List["t", " ", "z"]]]], RowBox[List[SuperscriptBox["t", "2"], "-", RowBox[List["2", " ", "t", " ", "z"]], "+", "1"]]], ",", RowBox[List["{", RowBox[List["t", ",", "0", ",", "n"]], "}"]]]], "]"]], "/;", RowBox[List[RowBox[List["-", "1"]], "<", "z", "<", "1"]]]]]]]]


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





2001-10-29