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 ArcCoth

 http://functions.wolfram.com/01.28.27.2706.01

 Input Form

 ArcCoth[Sqrt[z^2]] == ArcTanh[1/z] /; Inequality[-(Pi/2), Less, Arg[z], LessEqual, Pi/2]

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-09-04