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 ArcCosh

 http://functions.wolfram.com/01.26.27.1081.01

 Input Form

 ArcCosh[z] == (Pi I)/2 + I ArcCsc[Sqrt[1/z^2]] /; Pi/2 <= Arg[z] <= Pi

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCosh", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcCsc", "[", SqrtBox[FractionBox["1", SuperscriptBox["z", "2"]]], "]"]]]]]]]], "/;", RowBox[List[FractionBox["\[Pi]", "2"], "\[LessEqual]", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]]]]]]

 MathML Form

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

 Rule Form

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

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

 2003-08-21