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ExpIntegralE




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > ExpIntegralE[nu,z] > Integral transforms > Fourier sin transforms





http://functions.wolfram.com/06.34.22.0002.01









  


  








Input Form





FourierSinTransform[ExpIntegralE[\[Nu], t], t, x] == (Sqrt[Pi/2] Sign[x] Sec[(Pi \[Nu])/2])/(x^2)^(\[Nu]/2) + Sqrt[2/Pi] (1/(x (\[Nu] - 1))) HypergeometricPFQ[{1, (1 - \[Nu])/2}, {(3 - \[Nu])/2}, -(1/x^2)] /; Element[x, \[DoubleStruckCapitalR]] && Re[\[Nu]] > -1








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["FourierSinTransform", "[", RowBox[List[RowBox[List["ExpIntegralE", "[", RowBox[List["\[Nu]_", ",", "t_"]], "]"]], ",", "t_", ",", "x_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[SqrtBox[FractionBox["\[Pi]", "2"]], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["x", "2"], ")"]], RowBox[List["-", FractionBox["\[Nu]", "2"]]]], " ", RowBox[List["Sign", "[", "x", "]"]], " ", RowBox[List["Sec", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[Nu]"]], "2"], "]"]]]], "+", FractionBox[RowBox[List[SqrtBox[FractionBox["2", "\[Pi]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"]]], "}"]], ",", RowBox[List["{", FractionBox[RowBox[List["3", "-", "\[Nu]"]], "2"], "}"]], ",", RowBox[List["-", FractionBox["1", SuperscriptBox["x", "2"]]]]]], "]"]]]], RowBox[List["x", " ", RowBox[List["(", RowBox[List["\[Nu]", "-", "1"]], ")"]]]]]]], "/;", RowBox[List[RowBox[List["x", "\[Element]", "\[DoubleStruckCapitalR]"]], "&&", RowBox[List[RowBox[List["Re", "[", "\[Nu]", "]"]], ">", RowBox[List["-", "1"]]]]]]]]]]]]


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





2001-10-29