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 ExpIntegralEi

 http://functions.wolfram.com/06.35.02.0001.01

 Input Form

 ExpIntegralEi[z] == Sum[z^k/(k k!), {k, 1, Infinity}] + EulerGamma + (1/2) (Log[z] - Log[1/z])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ExpIntegralEi", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[SuperscriptBox["z", "k"], RowBox[List["k", " ", RowBox[List["k", "!"]]]]]]], "+", "EulerGamma", "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "z", "]"]], "-", RowBox[List["Log", "[", FractionBox["1", "z"], "]"]]]], ")"]]]]]]]]]]

 MathML Form

 Ei ( z ) k = 1 z k k k ! + TagBox["\[DoubledGamma]", Function[EulerGamma]] + 1 2 ( log ( z ) - log ( 1 z ) ) ExpIntegralEi z k 1 z k k k -1 1 2 z -1 1 z -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ExpIntegralEi", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[SuperscriptBox["z", "k"], RowBox[List["k", " ", RowBox[List["k", "!"]]]]]]], "+", "EulerGamma", "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "z", "]"]], "-", RowBox[List["Log", "[", FractionBox["1", "z"], "]"]]]], ")"]]]]]]]]]]

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

 2001-10-29

© 1998-2013 Wolfram Research, Inc.