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 ChebyshevT

 http://functions.wolfram.com/05.04.26.0019.01

 Input Form

 ChebyshevT[n, z] == Sqrt[Pi/2] (1 - z^2)^(1/4) LegendreP[n - 1/2, 1/2, 2, z]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ChebyshevT", "[", RowBox[List["n", ",", "z"]], "]"]], "\[Equal]", RowBox[List[SqrtBox[FractionBox["\[Pi]", "2"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["z", "2"]]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["LegendreP", "[", RowBox[List[RowBox[List["n", "-", FractionBox["1", "2"]]], ",", FractionBox["1", "2"], ",", "2", ",", "z"]], "]"]]]]]]]]

 MathML Form

 T n ( z ) π 2 1 - z 2 4 P TagBox["P", LegendreP] n - 1 2 1 2 ( z TagBox["z", HoldComplete[LegendreP, 2]] ) ChebyshevT n z 2 -1 1 2 1 -1 z 2 1 4 LegendreP n -1 1 2 1 2 2 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ChebyshevT", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SqrtBox[FractionBox["\[Pi]", "2"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["z", "2"]]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["LegendreP", "[", RowBox[List[RowBox[List["n", "-", FractionBox["1", "2"]]], ",", FractionBox["1", "2"], ",", "2", ",", "z"]], "]"]]]]]]]]

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

 2001-10-29