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ArcTanh






Mathematica Notation

Traditional Notation









Elementary Functions > ArcTanh[z] > Series representations > Generalized power series > Expansions at z==1 > For small integer powers of the function > For the second power





http://functions.wolfram.com/01.27.06.0047.01









  


  










Input Form





ArcTanh[z]^2 == (1/4) Log[(1 - z)/2]^2 - (1/4) Log[(1 - z)/2] (z - 1) Hypergeometric2F1[1, 1, 2, (1 - z)/2] + ((z - 1)^2/16) Hypergeometric2F1[1, 1, 2, (1 - z)/2]^2










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["ArcTanh", "[", "z_", "]"]], "2"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", SuperscriptBox[RowBox[List["Log", "[", FractionBox[RowBox[List["1", "-", "z"]], "2"], "]"]], "2"]]], "-", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "-", "z"]], "2"], "]"]], " ", RowBox[List["(", RowBox[List["z", "-", "1"]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List["1", ",", "1", ",", "2", ",", FractionBox[RowBox[List["1", "-", "z"]], "2"]]], "]"]]]], "+", RowBox[List[FractionBox["1", "16"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "1"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["Hypergeometric2F1", "[", RowBox[List["1", ",", "1", ",", "2", ",", FractionBox[RowBox[List["1", "-", "z"]], "2"]]], "]"]], "2"]]]]]]]]]










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





2007-05-02