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 ArcCosh

 http://functions.wolfram.com/01.26.27.1136.01

 Input Form

 ArcCosh[Sqrt[1 - z]] == (-I) ArcCsc[1/Sqrt[z]] /; Inequality[0, Less, Arg[z], LessEqual, Pi]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCosh", "[", SqrtBox[RowBox[List["1", "-", "z"]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["ArcCsc", "[", FractionBox["1", SqrtBox["z"]], "]"]]]]]], "/;", RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]]]]]]

 MathML Form

 cosh - 1 ( 1 - z ) - csc - 1 ( 1 z ) /; 0 < arg ( z ) π Condition 1 -1 z 1 2 -1 1 z 1 2 -1 Inequality 0 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCosh", "[", SqrtBox[RowBox[List["1", "-", "z_"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["ArcCsc", "[", FractionBox["1", SqrtBox["z"]], "]"]]]], "/;", RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]]]]]]]]

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

 2003-08-21