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http://functions.wolfram.com/06.35.10.0001.01
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ExpIntegralEi[z] == I Pi Sign[Im[z]] -
E^z (1/(1 - z -
(3 - z - 4/(5 - z - 9/(7 - z - 16/(9 - z - 25/(11 - z -
36/(13 - z + \[Ellipsis]))))))^(-1))) /; Abs[Arg[-z]] < Pi
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ExpIntegralEi", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["Sign", "[", RowBox[List["Im", "[", "z", "]"]], "]"]]]], " ", "-", RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], FractionBox["1", RowBox[List["1", "-", "z", "+", FractionBox[RowBox[List["-", "1"]], RowBox[List["3", "-", "z", "+", FractionBox[RowBox[List["-", "4"]], RowBox[List["5", "-", "z", "+", FractionBox[RowBox[List["-", "9"]], RowBox[List["7", "-", "z", "+", FractionBox[RowBox[List["-", "16"]], RowBox[List["9", "-", "z", "+", FractionBox[RowBox[List["-", "25"]], RowBox[List["11", "-", "z", "+", FractionBox[RowBox[List["-", "36"]], RowBox[List["13", "-", "z", "+", "\[Ellipsis]"]]]]]]]]]]]]]]]]]]]]]]]]]]], "/;", " ", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", RowBox[List["-", "z"]], "]"]], "]"]], "<", "\[Pi]"]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> Ei </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mi> sgn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> <mo> ⁢ </mo> <mfrac> <mn> 1 </mn> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> <mo> + </mo> <mstyle scriptlevel='0'> <mfrac> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mn> 3 </mn> <mo> - </mo> <mstyle scriptlevel='0'> <mi> z </mi> </mstyle> <mstyle scriptlevel='0'> <mo> + </mo> </mstyle> <mstyle scriptlevel='0'> <mfrac> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mrow> <mn> 5 </mn> <mo> - </mo> <mstyle scriptlevel='0'> <mi> z </mi> </mstyle> <mstyle scriptlevel='0'> <mo> + </mo> </mstyle> <mstyle scriptlevel='0'> <mfrac> <mrow> <mo> - </mo> <mn> 9 </mn> </mrow> <mrow> <mn> 7 </mn> <mo> - </mo> <mstyle scriptlevel='0'> <mi> z </mi> </mstyle> <mstyle scriptlevel='0'> <mo> + </mo> </mstyle> <mstyle scriptlevel='0'> <mfrac> <mrow> <mo> - </mo> <mn> 16 </mn> </mrow> <mrow> <mn> 9 </mn> <mo> - </mo> <mstyle scriptlevel='0'> <mi> z </mi> </mstyle> <mstyle scriptlevel='0'> <mo> + </mo> </mstyle> <mstyle scriptlevel='0'> <mfrac> <mrow> <mo> - </mo> <mn> 25 </mn> </mrow> <mrow> <mn> 11 </mn> <mo> - </mo> <mstyle scriptlevel='0'> <mi> z </mi> </mstyle> <mstyle scriptlevel='0'> <mo> + </mo> </mstyle> <mstyle scriptlevel='0'> <mfrac> <mrow> <mo> - </mo> <mn> 36 </mn> </mrow> <mrow> <mn> 13 </mn> <mo> - </mo> <mstyle scriptlevel='0'> <mi> z </mi> </mstyle> <mstyle scriptlevel='0'> <mo> + </mo> </mstyle> <mstyle scriptlevel='0'> <mo> … </mo> </mstyle> </mrow> </mfrac> </mstyle> </mrow> </mfrac> </mstyle> </mrow> </mfrac> </mstyle> </mrow> </mfrac> </mstyle> </mrow> </mfrac> </mstyle> </mrow> </mfrac> </mstyle> </mrow> </mfrac> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <mo> < </mo> <mi> π </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> ExpIntegralEi </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <imaginaryi /> <pi /> <apply> <ci> Sign </ci> <apply> <imaginary /> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -4 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 5 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -9 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 7 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -16 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 9 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -25 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 11 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -36 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 13 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <ci> … </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <lt /> <apply> <abs /> <apply> <arg /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> <pi /> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ExpIntegralEi", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["Sign", "[", RowBox[List["Im", "[", "z", "]"]], "]"]]]], "-", FractionBox[SuperscriptBox["\[ExponentialE]", "z"], RowBox[List["1", "-", "z", "-", FractionBox["1", RowBox[List["3", "-", "z", "-", FractionBox["4", RowBox[List["5", "-", "z", "-", FractionBox["9", RowBox[List["7", "-", "z", "-", FractionBox["16", RowBox[List["9", "-", "z", "-", FractionBox["25", RowBox[List["11", "-", "z", "-", FractionBox["36", RowBox[List["13", "-", "z", "+", "\[Ellipsis]"]]]]]]]]]]]]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", RowBox[List["-", "z"]], "]"]], "]"]], "<", "\[Pi]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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