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ExpIntegralE






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/06.34.22.0001.01









  


  










Input Form





FourierCosTransform[ExpIntegralE[\[Nu], t], t, x] == (Sqrt[Pi/2] Csc[(Pi \[Nu])/2])/(x^2)^(\[Nu]/2) + Sqrt[2/Pi] (1/(x^2 (\[Nu] - 2))) Hypergeometric2F1[1, 1 - \[Nu]/2, 2 - \[Nu]/2, -(1/x^2)] /; Element[x, \[DoubleStruckCapitalR]] && Re[\[Nu]] > 0










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["FourierCosTransform", "[", 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["Csc", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[Nu]"]], "2"], "]"]]]], "+", FractionBox[RowBox[List[SqrtBox[FractionBox["2", "\[Pi]"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List["1", ",", RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List["2", "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List["-", FractionBox["1", SuperscriptBox["x", "2"]]]]]], "]"]]]], RowBox[List[SuperscriptBox["x", "2"], " ", RowBox[List["(", RowBox[List["\[Nu]", "-", "2"]], ")"]]]]]]], "/;", RowBox[List[RowBox[List["x", "\[Element]", "\[DoubleStruckCapitalR]"]], "&&", RowBox[List[RowBox[List["Re", "[", "\[Nu]", "]"]], ">", "0"]]]]]]]]]]










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





2001-10-29





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