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 ArcTanh

 http://functions.wolfram.com/01.27.27.2474.01

 Input Form

 ArcTanh[1/Sqrt[1 - z]] == ArcCosh[1/Sqrt[z]] - (Pi I)/2 /; Inequality[-Pi, Less, Arg[z], LessEqual, 0]

 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["ArcCosh", "[", FractionBox["1", SqrtBox["z"]], "]"]], "-", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"]]]]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "0"]]]]]]]]

 MathML Form

 tanh - 1 ( 1 1 - z ) cosh - 1 ( 1 z ) - π 2 /; - π < arg ( z ) 0 Condition 1 1 -1 z 1 2 -1 1 z 1 2 -1 -1 2 -1 Inequality -1 z 0 [/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["ArcCosh", "[", FractionBox["1", SqrtBox["z"]], "]"]], "-", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"]]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "0"]]]]]]]]

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

 2003-08-21