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 ChebyshevT

 http://functions.wolfram.com/07.04.16.0006.01

 Input Form

 ChebyshevT[2 n, z] == (-1)^n ChebyshevT[n, 1 - 2 z^2] /; Element[n, Integers]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ChebyshevT", "[", RowBox[List[RowBox[List["2", "n"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], RowBox[List["ChebyshevT", "[", RowBox[List["n", ",", RowBox[List["1", "-", RowBox[List["2", SuperscriptBox["z", "2"]]]]]]], "]"]]]]]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]

 MathML Form

 T 2 n ( z ) ( - 1 ) n T n ( 1 - 2 z 2 ) /; n TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] Condition ChebyshevT 2 n z -1 n ChebyshevT n 1 -1 2 z 2 n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ChebyshevT", "[", RowBox[List[RowBox[List["2", " ", "n_"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List["ChebyshevT", "[", RowBox[List["n", ",", RowBox[List["1", "-", RowBox[List["2", " ", SuperscriptBox["z", "2"]]]]]]], "]"]]]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]]]

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

 2007-05-02