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 ArcTanh

 http://functions.wolfram.com/01.27.27.0029.01

 Input Form

 ArcTanh[Sqrt[(z - 1)/z]] == ArcCosh[Sqrt[z]] + ((Pi I)/2) (Sqrt[z] Sqrt[1/z] - 1)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcTanh", "[", SqrtBox[FractionBox[RowBox[List["z", "-", "1"]], "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["ArcCosh", "[", SqrtBox["z"], "]"]], "+", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["z"], " ", SqrtBox[FractionBox["1", "z"]]]], "-", "1"]], ")"]]]]]]]]]]

 MathML Form

 tanh - 1 ( z - 1 z ) cosh - 1 ( z ) + π 2 ( z 1 z - 1 ) z -1 z -1 1 2 z 1 2 2 -1 z 1 2 1 z -1 1 2 -1 [/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["ArcCosh", "[", SqrtBox["z"], "]"]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["z"], " ", SqrtBox[FractionBox["1", "z"]]]], "-", "1"]], ")"]]]]]]]]]]

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

 2001-10-29