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 ArcCoth

 http://functions.wolfram.com/01.28.27.2755.01

 Input Form

 ArcCoth[Sqrt[z^2 - 1] + z] == (1/2) ArcTanh[z] - (Pi Sqrt[-1 + z^2])/(4 Sqrt[1 - z^2])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcCoth", "[", RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]], "+", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", "2"], RowBox[List["ArcTanh", "[", "z", "]"]]]], "-", FractionBox[RowBox[List["\[Pi]", " ", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["z", "2"]]]]]], RowBox[List["4", " ", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]]]]]]]]]]

 MathML Form

 coth - 1 ( z 2 - 1 + z ) 1 2 tanh - 1 ( z ) - π z 2 - 1 4 1 - z 2 z 2 -1 1 2 z 1 2 z -1 z 2 -1 1 2 4 1 -1 z 2 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["z_", "2"], "-", "1"]]], "+", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["ArcTanh", "[", "z", "]"]], "2"], "-", FractionBox[RowBox[List["\[Pi]", " ", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["z", "2"]]]]]], RowBox[List["4", " ", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]]]]]]]]]]

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

 2003-09-04