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ExpIntegralE






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > ExpIntegralE[nu,z] > Series representations > Generalized power series > Expansions at z==0 > For the function itself > General case





http://functions.wolfram.com/06.34.06.0030.01









  


  










Input Form





ExpIntegralE[\[Nu], z] == Subscript[F, Infinity][z, \[Nu]] /; Subscript[F, n][z, \[Nu]] == Gamma[1 - \[Nu]] z^(\[Nu] - 1) - Sum[((-1)^k z^k)/((k - \[Nu] + 1) k!), {k, 0, n}] == z^(\[Nu] - 1) Gamma[1 - \[Nu], z] + (((-1)^n z^(n + 1))/((-2 - n + \[Nu]) (n + 1)!)) HypergeometricPFQ[{1, 2 + n - \[Nu]}, {2 + n, 3 + n - \[Nu]}, -z] && Element[n, Integers] && n >= 0










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[RowBox[List[SubscriptBox["F", "\[Infinity]"], "[", RowBox[List["z", ",", "\[Nu]"]], "]"]], "/;", RowBox[List[RowBox[List[RowBox[List[SubscriptBox["F", "n"], "[", RowBox[List["z", ",", "\[Nu]"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["1", "-", "\[Nu]"]], "]"]], " ", SuperscriptBox["z", RowBox[List["\[Nu]", "-", "1"]]]]], "-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", SuperscriptBox["z", "k"]]], RowBox[List[RowBox[List["(", RowBox[List["k", "-", "\[Nu]", "+", "1"]], ")"]], " ", RowBox[List["k", "!"]]]]]]]]], "\[Equal]", RowBox[List[RowBox[List[SuperscriptBox["z", RowBox[List["\[Nu]", "-", "1"]]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["1", "-", "\[Nu]"]], ",", "z"]], "]"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", SuperscriptBox["z", RowBox[List["n", "+", "1"]]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", RowBox[List["2", "+", "n", "-", "\[Nu]"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["2", "+", "n"]], ",", RowBox[List["3", "+", "n", "-", "\[Nu]"]]]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "-", "n", "+", "\[Nu]"]], ")"]], " ", RowBox[List[RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]], "!"]]]]]]]]], "&&", RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]










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





2007-05-02





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