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 ArcTanh

 http://functions.wolfram.com/01.27.27.2144.01

 Input Form

 ArcTanh[Sqrt[z/(z + 1)]] == ArcSinh[Sqrt[z]] /; !IntervalMemberQ[Interval[{-Infinity, -1}], z]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcTanh", "[", SqrtBox[FractionBox["z", RowBox[List["z", "+", "1"]]]], "]"]], "\[Equal]", RowBox[List["ArcSinh", "[", SqrtBox["z"], "]"]]]], "/;", RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", RowBox[List["-", "1"]]]], "}"]], "]"]], ",", " ", "z"]], "]"]], "]"]]]]]]

 MathML Form

 tanh - 1 ( z z + 1 ) sinh - 1 ( z ) /; z ( - , - 1 ) tanh - 1 ( z z + 1 ) sinh - 1 ( z ) /; z ( - , - 1 ) [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", SqrtBox[FractionBox["z_", RowBox[List["z_", "+", "1"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ArcSinh", "[", SqrtBox["z"], "]"]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", RowBox[List["-", "1"]]]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]

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

 2003-08-21