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 ArcTanh

 http://functions.wolfram.com/01.27.27.2431.01

 Input Form

 ArcTanh[1/Sqrt[z]] == -ArcCosh[Sqrt[-z]/Sqrt[1 - z]] /; Element[z, Reals] && z < 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcTanh", "[", FractionBox["1", SqrtBox["z"]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List["ArcCosh", "[", FractionBox[SqrtBox[RowBox[List["-", "z"]]], SqrtBox[RowBox[List["1", "-", "z"]]]], "]"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "\[And]", RowBox[List["z", "<", "0"]]]], ")"]]]]]]

 MathML Form

 tanh - 1 ( 1 z ) - cosh - 1 ( - z 1 - z ) /; ( z z < 0 ) Condition 1 z 1 2 -1 -1 -1 z 1 2 1 -1 z 1 2 -1 z z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", FractionBox["1", SqrtBox["z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", RowBox[List["ArcCosh", "[", FractionBox[SqrtBox[RowBox[List["-", "z"]]], SqrtBox[RowBox[List["1", "-", "z"]]]], "]"]]]], "/;", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "&&", RowBox[List["z", "<", "0"]]]]]]]]]]

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

 2003-08-21