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 ArcTanh

 http://functions.wolfram.com/01.27.06.0038.01

 Input Form

 ArcTanh[z]^2 == z^2 Sum[z^(2 k)/(2 k + 1), {k, 0, Infinity}]^2 /; Abs[z] < 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["ArcTanh", "[", "z", "]"]], "2"], "\[Equal]", RowBox[List[SuperscriptBox["z", "2"], SuperscriptBox[RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[SuperscriptBox["z", RowBox[List["2", " ", "k"]]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]]]], ")"]], "2"]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", "1"]]]]]]

 MathML Form

 tanh - 1 ( z ) 2 z 2 ( k = 0 z 2 k 2 k + 1 ) 2 /; "\[LeftBracketingBar]" z "\[RightBracketingBar]" < 1 Condition z 2 z 2 k 0 z 2 k 2 k 1 -1 2 z 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["ArcTanh", "[", "z_", "]"]], "2"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["z", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[SuperscriptBox["z", RowBox[List["2", " ", "k"]]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]]]], ")"]], "2"]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", "1"]]]]]]]]

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

 2007-05-02