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 ArcCoth

 http://functions.wolfram.com/01.28.27.1437.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-09-04