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 ArcCosh

 http://functions.wolfram.com/01.26.27.0752.01

 Input Form

 ArcCosh[z] == Pi I - I ArcCot[Sqrt[z^2]/Sqrt[1 - z^2]] /; Inequality[Pi/2, Less, Arg[z], LessEqual, Pi]

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21