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ArcTanh




Mathematica Notation

Traditional Notation









Elementary Functions > ArcTanh[z] > Integral representations > Contour integral representations





http://functions.wolfram.com/01.27.07.0003.01









  


  








Input Form





ArcTanh[z] == (-((I z)/(4 Pi^(3/2)))) ContourIntegrate[ (Gamma[s]^2 Gamma[1/2 - s] Gamma[1 - s])/(1 - z^2)^s, {s, \[ScriptCapitalL]}] /; Abs[Arg[1 - z^2]] < Pi








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "z"]], ")"]], " ", RowBox[List["ContourIntegrate", "[", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["Gamma", "[", "s", "]"]], "2"], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "-", "s"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", "s"]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["z", "2"]]], ")"]], RowBox[List["-", "s"]]]]], ",", RowBox[List["{", RowBox[List["s", ",", "\[ScriptCapitalL]"]], "}"]]]], "]"]]]], RowBox[List["4", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", RowBox[List["1", "-", SuperscriptBox["z", "2"]]], "]"]], "]"]], "<", "\[Pi]"]]]]]]]]


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





2001-10-29