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 Cosh

 http://functions.wolfram.com/01.20.16.0078.01

 Input Form

 Cosh[n (ArcSech[z]/2)] == ChebyshevT[n, (1/Sqrt[2]) Sqrt[(z + 1)/z]] /; Element[n, Integers] && n > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Cosh", "[", RowBox[List["n", " ", FractionBox[RowBox[List["ArcSech", "[", "z", "]"]], "2"]]], "]"]], "\[Equal]", RowBox[List["ChebyshevT", "[", RowBox[List["n", ",", RowBox[List[FractionBox["1", SqrtBox["2"]], SqrtBox[FractionBox[RowBox[List["z", "+", "1"]], "z"]]]]]], "]"]]]], "/;", RowBox[List[RowBox[List["Element", "[", RowBox[List["n", ",", "Integers"]], "]"]], "\[And]", RowBox[List["n", ">", "0"]]]]]]]]

 MathML Form

 cosh ( n 2 sech - 1 ( z ) ) T n ( 1 2 z + 1 z ) /; n + Condition n 2 -1 z ChebyshevT n 1 2 1 2 -1 z 1 z -1 1 2 n SuperPlus [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Cosh", "[", RowBox[List[FractionBox["1", "2"], " ", "n_", " ", RowBox[List["ArcSech", "[", "z_", "]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ChebyshevT", "[", RowBox[List["n", ",", FractionBox[SqrtBox[FractionBox[RowBox[List["z", "+", "1"]], "z"]], SqrtBox["2"]]]], "]"]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]]]]]]]]]]

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

 2001-10-29