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ArcCoth






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.28.07.0003.01









  


  










Input Form





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










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





2001-10-29





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