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 ArcCosh

 http://functions.wolfram.com/01.26.27.2263.01

 Input Form

 ArcCosh[Sqrt[-1 - z^2]/Sqrt[-z^2]] == ArcCsch[z] /; Inequality[-(Pi/2), LessEqual, Arg[z], Less, Pi/2]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCosh", "[", FractionBox[SqrtBox[RowBox[List[RowBox[List["-", "1"]], "-", SuperscriptBox["z", "2"]]]], SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]], "]"]], "\[Equal]", RowBox[List["ArcCsch", "[", "z", "]"]]]], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "\[LessEqual]", RowBox[List["Arg", "[", "z", "]"]], "<", FractionBox["\[Pi]", "2"]]]]]]]

 MathML Form

 cosh - 1 ( - z 2 - 1 - z 2 ) csch - 1 ( z ) /; - π 2 arg ( z ) < π 2 Condition -1 z 2 -1 1 2 -1 z 2 1 2 -1 z Inequality -1 2 -1 z 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCosh", "[", FractionBox[SqrtBox[RowBox[List[RowBox[List["-", "1"]], "-", SuperscriptBox["z_", "2"]]]], SqrtBox[RowBox[List["-", SuperscriptBox["z_", "2"]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ArcCsch", "[", "z", "]"]], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "\[LessEqual]", RowBox[List["Arg", "[", "z", "]"]], "<", FractionBox["\[Pi]", "2"]]]]]]]]]

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

 2003-08-21