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 ArcCoth

 http://functions.wolfram.com/01.28.27.3402.01

 Input Form

 ArcCoth[Sqrt[(z - 1)/z]] == ArcSech[Sqrt[1/z]] - (Pi I)/2 /; Inequality[0, LessEqual, Arg[z], Less, Pi]

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-09-04