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 ArcCoth

 http://functions.wolfram.com/01.28.27.2534.01

 Input Form

 ArcCoth[Sqrt[1/(1 - z)]] == ArcCosh[Sqrt[1/z]] - Pi I /; Element[z, Reals] && z < 0

 Standard Form

 Cell[BoxData[RowBox[List[" ", RowBox[List[RowBox[List[RowBox[List["ArcCoth", "[", SqrtBox[FractionBox["1", RowBox[List["1", "-", "z"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["ArcCosh", "[", SqrtBox[FractionBox["1", "z"]], "]"]], "-", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "\[And]", RowBox[List["z", "<", "0"]]]], ")"]]]]]]]]

 MathML Form

 coth - 1 ( 1 1 - z ) cosh - 1 ( 1 z ) - π /; ( z z < 0 ) Condition 1 1 -1 z -1 1 2 1 z -1 1 2 -1 z z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", SqrtBox[FractionBox["1", RowBox[List["1", "-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["ArcCosh", "[", SqrtBox[FractionBox["1", "z"]], "]"]], "-", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]]]], "/;", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "&&", RowBox[List["z", "<", "0"]]]]]]]]]]

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

 2003-09-04