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 Sinh

 http://functions.wolfram.com/01.19.16.0054.01

 Input Form

 Sinh[n ArcCsch[z]] == (1/z) ChebyshevU[n - 1, Sqrt[1 + 1/z^2]] /; Element[n, Integers] && n > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Sinh", "[", RowBox[List["n", " ", RowBox[List["ArcCsch", "[", "z", "]"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "z"], RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["n", "-", "1"]], ",", SqrtBox[RowBox[List["1", "+", FractionBox["1", SuperscriptBox["z", "2"]]]]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["Element", "[", RowBox[List["n", ",", "Integers"]], "]"]], "\[And]", RowBox[List["n", ">", "0"]]]]]]]]

 MathML Form

 sinh ( n csch - 1 ( z ) ) 1 z U n - 1 ( 1 + 1 z 2 ) /; n + Condition n z 1 z -1 ChebyshevU n -1 1 1 z 2 -1 1 2 n SuperPlus [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Sinh", "[", RowBox[List["n_", " ", RowBox[List["ArcCsch", "[", "z_", "]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["n", "-", "1"]], ",", SqrtBox[RowBox[List["1", "+", FractionBox["1", SuperscriptBox["z", "2"]]]]]]], "]"]], "z"], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]]]]]]]]]]

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

 2001-10-29