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 ArcCosh

 http://functions.wolfram.com/01.26.27.0743.01

 Input Form

 ArcCosh[z] == (3 Pi I)/2 + I ArcCot[Sqrt[(1 - z^2)/z^2]] /; Element[z, Reals] && z < -1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCosh", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["3", "\[Pi]", " ", "\[ImaginaryI]"]], "2"], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcCot", "[", SqrtBox[FractionBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]], SuperscriptBox["z", "2"]]], "]"]]]]]]]], "/;", " ", RowBox[List["(", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "\[And]", RowBox[List["z", "<", RowBox[List["-", "1"]]]]]], ")"]]]]]]

 MathML Form

 cosh - 1 ( z ) 3 π 2 + cot - 1 ( 1 - z 2 z 2 ) /; ( z z < - 1 ) Condition z 3 2 -1 1 -1 z 2 z 2 -1 1 2 z z -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCosh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List["3", " ", "\[Pi]", " ", "\[ImaginaryI]"]], "2"], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcCot", "[", SqrtBox[FractionBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]], SuperscriptBox["z", "2"]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "&&", RowBox[List["z", "<", RowBox[List["-", "1"]]]]]]]]]]]]

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

 2003-08-21