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 ArcTanh

 http://functions.wolfram.com/01.27.27.2118.01

 Input Form

 ArcTanh[1/Sqrt[1 + z]] == -ArcSinh[Sqrt[1/z]] /; Element[z, Reals] && z < -1

 Standard Form

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

 MathML Form

 tanh - 1 ( 1 1 + z ) - sinh - 1 ( 1 z ) /; ( z z < - 1 ) Condition 1 1 z 1 2 -1 -1 1 z -1 1 2 z z -1 [/itex]

 Rule Form

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

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

 2003-08-21