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 ArcTanh

 http://functions.wolfram.com/01.27.27.3254.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcTanh", "[", FractionBox[StyleBox["1", "Program"], SqrtBox["z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", "2"], RowBox[List["ArcSech", "[", FractionBox[RowBox[List["1", "-", "z"]], RowBox[List["1", "+", "z"]]], "]"]]]], "-", RowBox[List[SqrtBox["z"], SqrtBox[RowBox[List["-", FractionBox["1", "z"]]]], FractionBox["\[Pi]", "2"]]]]]]]]]

 MathML Form

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

 Rule Form

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

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

 2003-08-21