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CoshIntegral






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > CoshIntegral[z] > Integral representations > Contour integral representations





http://functions.wolfram.com/06.40.07.0002.01









  


  










Input Form





CoshIntegral[z] == (-(Sqrt[Pi]/(4 Pi I))) ContourIntegrate[ Gamma[s]^2/(Gamma[1 + s] Gamma[1/2 - s])/(-(z^2/4))^s, {s, \[ScriptCapitalL]}] - (1/2) (Log[-z^2] - 2 Log[z])










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["CoshIntegral", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["ContourIntegrate", "[", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["Gamma", "[", "s", "]"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[SuperscriptBox["z", "2"], "4"]]], ")"]], RowBox[List["-", "s"]]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List["1", "+", "s"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "-", "s"]], "]"]]]]], ",", RowBox[List["{", RowBox[List["s", ",", "\[ScriptCapitalL]"]], "}"]]]], "]"]]]], RowBox[List["4", " ", "\[Pi]", " ", "\[ImaginaryI]"]]]]], "-", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["-", SuperscriptBox["z", "2"]]], "]"]], "-", RowBox[List["2", " ", RowBox[List["Log", "[", "z", "]"]]]]]], ")"]]]]]]]]]]










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





2001-10-29