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 ArcCosh

 http://functions.wolfram.com/01.26.27.2156.01

 Input Form

 ArcCosh[z] == (Pi I)/4 + (1/2) ArcCsch[I/(2 z^2 - 1)] /; Inequality[0, Less, Arg[z], LessEqual, Pi/2]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCosh", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "4"], "+", RowBox[List[FractionBox["1", "2"], RowBox[List["ArcCsch", "[", FractionBox["\[ImaginaryI]", RowBox[List[RowBox[List["2", SuperscriptBox["z", "2"]]], "-", "1"]]], "]"]]]]]]]], "/;", RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox["\[Pi]", "2"]]]]]]]

 MathML Form

 cosh - 1 ( z ) π 4 + 1 2 csch - 1 ( 2 z 2 - 1 ) /; 0 < arg ( z ) π 2 Condition z 4 -1 1 2 2 z 2 -1 -1 Inequality 0 z 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCosh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "4"], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["ArcCsch", "[", FractionBox["\[ImaginaryI]", RowBox[List[RowBox[List["2", " ", SuperscriptBox["z", "2"]]], "-", "1"]]], "]"]]]]]], "/;", RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox["\[Pi]", "2"]]]]]]]]]

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

 2003-08-21