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 ExpIntegralEi

 http://functions.wolfram.com/06.35.06.0010.01

 Input Form

 ExpIntegralEi[x] == (-E^x) Sum[LaguerreL[k, -x]/(k + 1), {k, 0, Infinity}] /; x < 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ExpIntegralEi", "[", "x", "]"]], "\[Equal]", RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", "x"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List["LaguerreL", "[", RowBox[List["k", ",", RowBox[List["-", "x"]]]], "]"]], RowBox[List["k", "+", "1"]]]]]]]]], "/;", RowBox[List["x", "<", "0"]]]]]]

 MathML Form

 Ei ( x ) - x k = 0 L k ( - x ) k + 1 /; x < 0 Condition ExpIntegralEi x -1 x k 0 LaguerreL k -1 x k 1 -1 x 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ExpIntegralEi", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", "x"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List["LaguerreL", "[", RowBox[List["k", ",", RowBox[List["-", "x"]]]], "]"]], RowBox[List["k", "+", "1"]]]]]]], "/;", RowBox[List["x", "<", "0"]]]]]]]]

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

 2001-10-29