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 Cosh

 http://functions.wolfram.com/01.20.16.0058.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Cosh", "[", RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", "n_", " ", RowBox[List["ArcCos", "[", "z_", "]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ChebyshevT", "[", RowBox[List["n", ",", FractionBox[SqrtBox[RowBox[List["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