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FresnelS






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/06.32.07.0003.01









  


  










Input Form





FresnelS[z] == ((Pi z^(9/4))/(Sqrt[2] (z^2)^(3/4) (-z)^(3/4))) (1/(2 Pi I)) ContourIntegrate[Gamma[s + 3/4]/(Gamma[s + 1] Gamma[3/4 - s] Gamma[1 - s])/ ((-(Pi^2/16)) z^4)^s, {s, \[ScriptCapitalL]}]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["FresnelS", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["\[Pi]", " ", SuperscriptBox["z", RowBox[List["9", "/", "4"]]]]], ")"]], " ", RowBox[List["ContourIntegrate", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["s", "+", FractionBox["3", "4"]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[FractionBox["1", "16"], " ", RowBox[List["(", RowBox[List["-", SuperscriptBox["\[Pi]", "2"]]], ")"]], " ", SuperscriptBox["z", "4"]]], ")"]], RowBox[List["-", "s"]]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List["s", "+", "1"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["3", "4"], "-", "s"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", "s"]], "]"]]]]], ",", RowBox[List["{", RowBox[List["s", ",", "\[ScriptCapitalL]"]], "}"]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "2"], ")"]], RowBox[List["3", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["3", "/", "4"]]]]], ")"]], " ", RowBox[List["(", RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]"]], ")"]]]]]]]]]










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





2001-10-29





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