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 ChebyshevU

 http://functions.wolfram.com/05.05.06.0032.01

 Input Form

 ChebyshevU[n, z] == (1/Sqrt[1 - z^2]) Sin[2 (1 + n) ArcSin[Sqrt[1 - z]/Sqrt[2]]]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ChebyshevU", "[", RowBox[List["n", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]], RowBox[List["Sin", "[", RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]], " ", RowBox[List["ArcSin", "[", FractionBox[SqrtBox[RowBox[List["1", "-", "z"]]], SqrtBox["2"]], "]"]]]], "]"]]]]]]]]

 MathML Form

 U n ( z ) 1 1 - z 2 sin ( 2 ( n + 1 ) sin - 1 ( 1 - z 2 ) ) ChebyshevU n z 1 1 -1 z 2 1 2 -1 2 n 1 1 -1 z 1 2 2 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ChebyshevU", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["Sin", "[", RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]], " ", RowBox[List["ArcSin", "[", FractionBox[SqrtBox[RowBox[List["1", "-", "z"]]], SqrtBox["2"]], "]"]]]], "]"]], SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]]]]]]

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

 2007-05-02