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 ArcTanh

 http://functions.wolfram.com/01.27.27.0995.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21