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 ArcCosh

 http://functions.wolfram.com/01.26.27.0876.01

 Input Form

 ArcCosh[(z + 1)/(z - 1)] == Pi I - 2 I ArcCot[1/Sqrt[-z]] /; Im[z] <= 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCosh", "[", FractionBox[RowBox[List["z", "+", "1"]], RowBox[List["z", "-", "1"]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], " ", "-", RowBox[List["2", "\[ImaginaryI]", " ", RowBox[List["ArcCot", "[", FractionBox["1", SqrtBox[RowBox[List["-", "z"]]]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[LessEqual]", "0"]]]]]]

 MathML Form

 cosh - 1 ( z + 1 z - 1 ) π - 2 cot - 1 ( 1 - z ) /; Im ( z ) 0 Condition z 1 z -1 -1 -1 2 1 -1 z 1 2 -1 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCosh", "[", FractionBox[RowBox[List["z_", "+", "1"]], RowBox[List["z_", "-", "1"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["ArcCot", "[", FractionBox["1", SqrtBox[RowBox[List["-", "z"]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[LessEqual]", "0"]]]]]]]]

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

 2003-08-21