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ExpIntegralE






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > ExpIntegralE[nu,z] > Continued fraction representations





http://functions.wolfram.com/06.34.10.0002.01









  


  










Input Form





ExpIntegralE[\[Nu], z] == 1/(E^z (z + ContinueFraction[{2^((-1 - (-1)^k)/2) k^((1 + (-1)^k)/2) ((k - 1)/2 + \[Nu])^((1 - (-1)^k)/2), z^(((-1)^k + 1)/2)}, {k, 1, Infinity}])) /; !IntervalMemberQ[Interval[{-Infinity, 0}], z]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ExpIntegralE", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], RowBox[List["z", "+", RowBox[List["ContinueFraction", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"]]], ")"]]]]], " ", SuperscriptBox["k", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"]]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[FractionBox[RowBox[List["k", "-", "1"]], "2"], "+", "\[Nu]"]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"]]], ")"]]]]]]], ",", SuperscriptBox["z", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], "+", "1"]], ")"]]]]]]], "}"]], ",", RowBox[List["{", RowBox[List["k", ",", "1", ",", "\[Infinity]"]], "}"]]]], "]"]]]]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]










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





2001-10-29





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