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 ArcTanh

 http://functions.wolfram.com/01.27.16.0063.01

 Input Form

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

 Standard Form

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

 MathML Form

 tanh - 1 ( 2 z z + 1 ) 2 tanh - 1 ( 1 z ) + π - 1 z z /; "\[LeftBracketingBar]" z "\[RightBracketingBar]" < 1 Condition 2 z 1 2 z 1 -1 2 1 z 1 2 -1 -1 1 z -1 1 2 z 1 2 z 1 [/itex]

 Rule Form

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

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

 2003-08-21