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 ArcTanh

 http://functions.wolfram.com/01.27.06.0012.02

 Input Form

 ArcTanh[z] \[Proportional] -(Log[2]/2) + (1/2) Log[z + 1] + (z + 1)/4 + O[(z + 1)^2]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcTanh", "[", "z", "]"]], "\[Proportional]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["Log", "[", "2", "]"]], "2"]]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Log", "[", RowBox[List["z", "+", "1"]], "]"]]]], "+", FractionBox[RowBox[List["z", "+", "1"]], "4"], "+", RowBox[List["O", "[", SuperscriptBox[RowBox[List["(", RowBox[List["z", "+", "1"]], ")"]], "2"], "]"]]]]]]]]

 MathML Form

 tanh - 1 ( z ) - log ( 2 ) 2 + 1 2 log ( z + 1 ) + z + 1 4 + O ( ( z + 1 ) 2 ) Proportional z -1 2 2 -1 1 2 z 1 z 1 4 -1 O z 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["Log", "[", "2", "]"]], "2"]]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Log", "[", RowBox[List["z", "+", "1"]], "]"]]]], "+", FractionBox[RowBox[List["z", "+", "1"]], "4"], "+", SuperscriptBox[RowBox[List["O", "[", RowBox[List["z", "+", "1"]], "]"]], "2"]]]]]]]

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

 2001-10-29