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 ArcTanh

 http://functions.wolfram.com/01.27.27.2649.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21