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ExpIntegralEi






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > ExpIntegralEi[z] > Complex characteristics > Real part





http://functions.wolfram.com/06.35.19.0001.01









  


  










Input Form





Re[ExpIntegralEi[x + I y]] == x Sum[(((-1)^j y^(2 j))/((1 + 2 j) (2 j)!)) HypergeometricPFQ[{1/2 + j}, {3/2, 3/2 + j}, x^2/4], {j, 0, Infinity}] - Sum[(((-1)^j y^(2 + 2 j))/(2 (1 + j) (2 + 2 j)!)) HypergeometricPFQ[{1 + j}, {1/2, 2 + j}, x^2/4], {j, 0, Infinity}] + (1/2) Log[x^2 + y^2] + CoshIntegral[x] - Log[x]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Re", "[", RowBox[List["ExpIntegralEi", "[", RowBox[List["x_", "+", RowBox[List["\[ImaginaryI]", " ", "y_"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["x", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "j"], " ", SuperscriptBox["y", RowBox[List["2", " ", "j"]]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], "+", "j"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", RowBox[List[FractionBox["3", "2"], "+", "j"]]]], "}"]], ",", FractionBox[SuperscriptBox["x", "2"], "4"]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "j"]]]], ")"]], " ", RowBox[List[RowBox[List["(", RowBox[List["2", " ", "j"]], ")"]], "!"]]]]]]]]], "-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "j"], " ", SuperscriptBox["y", RowBox[List["2", "+", RowBox[List["2", " ", "j"]]]]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", "+", "j"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["2", "+", "j"]]]], "}"]], ",", FractionBox[SuperscriptBox["x", "2"], "4"]]], "]"]]]], RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", "j"]], ")"]], " ", RowBox[List[RowBox[List["(", RowBox[List["2", "+", RowBox[List["2", " ", "j"]]]], ")"]], "!"]]]]]]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Log", "[", RowBox[List[SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"]]], "]"]]]], "+", RowBox[List["CoshIntegral", "[", "x", "]"]], "-", RowBox[List["Log", "[", "x", "]"]]]]]]]]










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





2001-10-29





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