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ExpIntegralE




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > ExpIntegralE[nu,z] > Continued fraction representations





http://functions.wolfram.com/06.34.10.0001.01









  


  








Input Form





ExpIntegralE[\[Nu], z] == 1/ (E^z (z + \[Nu]/(1 + 1/(z + (\[Nu] + 1)/ (1 + 2/(z + (\[Nu] + 2)/(1 + 3/(z + \[Ellipsis])))))))) /; !IntervalMemberQ[Interval[{-Infinity, 0}], z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ExpIntegralE", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", FractionBox[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], RowBox[List["z", "+", FractionBox["\[Nu]", RowBox[List["1", "+", FractionBox["1", RowBox[List["z", "+", FractionBox[RowBox[List["\[Nu]", "+", "1"]], RowBox[List["1", "+", FractionBox["2", RowBox[List["z", "+", FractionBox[RowBox[List["\[Nu]", "+", "2"]], RowBox[List["1", "+", FractionBox["3", RowBox[List["z", "+", "\[Ellipsis]"]]]]]]]]]]]]]]]]]]]]]]], "/;", RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]], "]"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msub> <semantics> <mi> E </mi> <annotation encoding='Mathematica'> TagBox[&quot;E&quot;, ExpIntegralE] </annotation> </semantics> <mi> &#957; </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msup> <mrow> <mi> z </mi> <mo> + </mo> <mstyle scriptlevel='0'> <mfrac> <mi> &#957; </mi> <mstyle scriptlevel='0'> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 1 </mn> <mstyle scriptlevel='0'> <mrow> <mi> z </mi> <mo> + </mo> <mfrac> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 2 </mn> <mstyle scriptlevel='0'> <mrow> <mi> z </mi> <mo> + </mo> <mfrac> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 3 </mn> <mstyle scriptlevel='0'> <mrow> <mi> z </mi> <mo> + </mo> <mo> &#8230; </mo> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mstyle> </mrow> </mfrac> </mrow> <mo> /; </mo> <mrow> <mi> z </mi> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8734; </mi> </mrow> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <msub> <semantics> <mi> E </mi> <annotation encoding='Mathematica'> TagBox[&quot;E&quot;, ExpIntegralE] </annotation> </semantics> <mi> &#957; </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msup> <mrow> <mi> z </mi> <mo> + </mo> <mstyle scriptlevel='0'> <mfrac> <mi> &#957; </mi> <mstyle scriptlevel='0'> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 1 </mn> <mstyle scriptlevel='0'> <mrow> <mi> z </mi> <mo> + </mo> <mfrac> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 2 </mn> <mstyle scriptlevel='0'> <mrow> <mi> z </mi> <mo> + </mo> <mfrac> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 3 </mn> <mstyle scriptlevel='0'> <mrow> <mi> z </mi> <mo> + </mo> <mo> &#8230; </mo> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mstyle> </mrow> </mfrac> </mrow> <mo> /; </mo> <mrow> <mi> z </mi> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8734; </mi> </mrow> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ExpIntegralE", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], RowBox[List["z", "+", FractionBox["\[Nu]", RowBox[List["1", "+", FractionBox["1", RowBox[List["z", "+", FractionBox[RowBox[List["\[Nu]", "+", "1"]], RowBox[List["1", "+", FractionBox["2", RowBox[List["z", "+", FractionBox[RowBox[List["\[Nu]", "+", "2"]], RowBox[List["1", "+", FractionBox["3", RowBox[List["z", "+", "\[Ellipsis]"]]]]]]]]]]]]]]]]]]]]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]


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





2001-10-29