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 ArcCosh

 http://functions.wolfram.com/01.26.27.1943.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21