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ArcSech




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.30.07.0004.01









  


  








Input Form





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


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





2001-10-29