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ExpIntegralE




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/06.34.10.0007.01









  


  








Input Form





ExpIntegralE[\[Nu], z] == z^(\[Nu] - 1) Gamma[1 - \[Nu]] - 1/(E^z (1 - \[Nu] - ((1 - \[Nu]) z)/(2 - \[Nu] + z - ((2 - \[Nu]) z)/(3 - \[Nu] + z - ((3 - \[Nu]) z)/(4 - \[Nu] + z - ((4 - \[Nu]) z)/(5 - \[Nu] + z - ((5 - \[Nu]) z)/(6 - \[Nu] + z + \[Ellipsis])))))))








Standard Form





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MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <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> <mrow> <mrow> <msup> <mi> z </mi> <mrow> <mi> &#957; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#957; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mtext> </mtext> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msup> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#957; </mi> <mo> - </mo> <mstyle scriptlevel='0'> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#957; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mrow> <mn> 2 </mn> <mstyle scriptlevel='0'> <mo> - </mo> </mstyle> <mstyle scriptlevel='0'> <mi> &#957; </mi> </mstyle> <mstyle scriptlevel='0'> <mo> + </mo> </mstyle> <mstyle scriptlevel='0'> <mi> z </mi> </mstyle> <mstyle scriptlevel='0'> <mo> - </mo> </mstyle> <mstyle scriptlevel='0'> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> - </mo> <mi> &#957; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mrow> <mn> 3 </mn> <mstyle scriptlevel='0'> <mo> - </mo> </mstyle> <mstyle scriptlevel='0'> <mi> &#957; </mi> </mstyle> <mstyle scriptlevel='0'> <mo> + </mo> </mstyle> <mstyle scriptlevel='0'> <mi> z </mi> </mstyle> <mstyle scriptlevel='0'> <mo> - </mo> </mstyle> <mstyle scriptlevel='0'> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> - </mo> <mi> &#957; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mrow> <mn> 4 </mn> <mstyle scriptlevel='0'> <mo> - </mo> </mstyle> <mstyle scriptlevel='0'> <mi> &#957; </mi> </mstyle> <mstyle scriptlevel='0'> <mo> + </mo> </mstyle> <mstyle scriptlevel='0'> <mi> z </mi> </mstyle> <mstyle scriptlevel='0'> <mo> - </mo> </mstyle> <mstyle scriptlevel='0'> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> - </mo> <mi> &#957; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mrow> <mn> 5 </mn> <mstyle scriptlevel='0'> <mo> - </mo> </mstyle> <mstyle scriptlevel='0'> <mi> &#957; </mi> </mstyle> <mstyle scriptlevel='0'> <mo> + </mo> </mstyle> <mstyle scriptlevel='0'> <mi> z </mi> </mstyle> <mstyle scriptlevel='0'> <mo> - </mo> </mstyle> <mstyle scriptlevel='0'> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 5 </mn> <mo> - </mo> <mi> &#957; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mrow> <mn> 6 </mn> <mstyle scriptlevel='0'> <mo> - </mo> </mstyle> <mstyle scriptlevel='0'> <mi> &#957; </mi> </mstyle> <mstyle scriptlevel='0'> <mo> + </mo> </mstyle> <mstyle scriptlevel='0'> <mi> z </mi> </mstyle> <mstyle scriptlevel='0'> <mo> + </mo> </mstyle> <mstyle scriptlevel='0'> <mo> &#8230; </mo> </mstyle> </mrow> </mfrac> </mstyle> </mrow> </mfrac> </mstyle> </mrow> </mfrac> </mstyle> </mrow> </mfrac> </mstyle> </mrow> </mfrac> </mstyle> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> ExpIntegralE </ci> <ci> &#957; </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> <ci> z </ci> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> <ci> z </ci> <apply> <power /> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> <ci> z </ci> <apply> <power /> <apply> <plus /> <cn type='integer'> 4 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <cn type='integer'> 4 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> <ci> z </ci> <apply> <power /> <apply> <plus /> <cn type='integer'> 5 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <cn type='integer'> 5 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> <ci> z </ci> <apply> <power /> <apply> <plus /> <cn type='integer'> 6 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <ci> z </ci> <ci> &#8230; </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29