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 ArcTanh

 http://functions.wolfram.com/01.27.27.2231.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21