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 ArcCoth

 http://functions.wolfram.com/01.28.27.0670.01

 Input Form

 ArcCoth[Sqrt[z - 1]/Sqrt[z]] == (Pi I)/2 - I ArcCos[Sqrt[z]] /; Im[z] < 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCoth", "[", FractionBox[SqrtBox[RowBox[List["z", "-", "1"]]], SqrtBox["z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcCos", "[", SqrtBox["z"], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "<", "0"]]]]]]

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", FractionBox[SqrtBox[RowBox[List["z_", "-", "1"]]], SqrtBox["z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcCos", "[", SqrtBox["z"], "]"]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "<", "0"]]]]]]]]

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

 2003-09-04