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ExpIntegralEi






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > ExpIntegralEi[z] > Series representations > Generalized power series > Expansions at generic point z==z0 > For the function itself





http://functions.wolfram.com/06.35.06.0016.01









  


  










Input Form





ExpIntegralEi[z] == ExpIntegralEi[Subscript[z, 0]] + (1/2) (Log[1/Subscript[z, 0]] - Log[Subscript[z, 0]]) - I Pi Floor[(Pi + Arg[z])/(2 Pi)] + Floor[Arg[z - Subscript[z, 0]]/(2 Pi)] (Log[Subscript[z, 0]] + Log[1/Subscript[z, 0]]) + Log[Subscript[z, 0]] + Sum[((-1)^(k - 1)/(Subscript[z, 0]^k k) + (Subscript[z, 0]^(1 - k)/k!) HypergeometricPFQRegularized[{1, 1}, {2, 2 - k}, Subscript[z, 0]]) (z - Subscript[z, 0])^k, {k, 1, Infinity}]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ExpIntegralEi", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ExpIntegralEi", "[", SubscriptBox["zz", "0"], "]"]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", FractionBox["1", SubscriptBox["zz", "0"]], "]"]], "-", RowBox[List["Log", "[", SubscriptBox["zz", "0"], "]"]]]], ")"]]]], "-", RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "+", RowBox[List["Arg", "[", "z", "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], "+", RowBox[List[RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", SubscriptBox["zz", "0"], "]"]], "+", RowBox[List["Log", "[", FractionBox["1", SubscriptBox["zz", "0"]], "]"]]]], ")"]]]], "+", RowBox[List["Log", "[", SubscriptBox["zz", "0"], "]"]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["k", "-", "1"]]], " ", SubsuperscriptBox["zz", "0", RowBox[List["-", "k"]]]]], "k"], "+", FractionBox[RowBox[List[SubsuperscriptBox["zz", "0", RowBox[List["1", "-", "k"]]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", "1"]], "}"]], ",", RowBox[List["{", RowBox[List["2", ",", RowBox[List["2", "-", "k"]]]], "}"]], ",", SubscriptBox["zz", "0"]]], "]"]]]], RowBox[List["k", "!"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]], "k"]]]]]]]]]]]










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





2007-05-02