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 ArcTanh

 http://functions.wolfram.com/01.27.16.0076.01

 Input Form

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

 Standard Form

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

 MathML Form

 tanh - 1 ( z + 1 2 z ) 2 tanh - 1 ( z ) - π z - 1 2 1 - z z 1 2 z 1 2 -1 2 z 1 2 -1 z -1 1 2 2 1 -1 z 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", FractionBox[RowBox[List["1", "+", "z_"]], RowBox[List["2", " ", SqrtBox["z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["2", " ", RowBox[List["ArcTanh", "[", SqrtBox["z"], "]"]]]], "-", FractionBox[RowBox[List["\[Pi]", " ", SqrtBox[RowBox[List["z", "-", "1"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]]]

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

 2003-08-21