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 ArcTanh

 http://functions.wolfram.com/01.27.27.2135.01

 Input Form

 ArcTanh[Sqrt[(z + 1)/z]] == (Pi I)/2 - ArcSinh[Sqrt[z]] /; Element[z, Reals] && -1 < z < 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcTanh", "[", SqrtBox[FractionBox[RowBox[List["z", "+", "1"]], "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "-", RowBox[List["ArcSinh", "[", SqrtBox["z"], "]"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "\[And]", RowBox[List[RowBox[List["-", "1"]], "<", "z", "<", "0"]]]], ")"]]]]]]

 MathML Form

 tanh - 1 ( z + 1 z ) π 2 - sinh - 1 ( z ) /; ( z - 1 < z < 0 ) Condition z 1 z -1 1 2 2 -1 -1 z 1 2 z -1 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", SqrtBox[FractionBox[RowBox[List["z_", "+", "1"]], "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "-", RowBox[List["ArcSinh", "[", SqrtBox["z"], "]"]]]], "/;", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "&&", RowBox[List[RowBox[List["-", "1"]], "<", "z", "<", "0"]]]]]]]]]]

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

 2003-08-21