Exponential integral E: Representations through equivalent functions (formula 06.34.27.0001)

ExpIntegralE

$Mathematica Notation$

Gamma, Beta, Erf

ExpIntegralE[nu,z]

Representations through equivalent functions

With inverse function

http://functions.wolfram.com/06.34.27.0001.01

Input Form

ExpIntegralE[\[Nu], InverseGammaRegularized[1 - \[Nu], z]] == InverseGammaRegularized[1 - \[Nu], z]^(\[Nu] - 1) Gamma[1 - \[Nu]] z

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["ExpIntegralE", "[", RowBox[List["\[Nu]", ",", RowBox[List["InverseGammaRegularized", "[", RowBox[List[RowBox[List["1", "-", "\[Nu]"]], ",", "z"]], "]"]]]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["InverseGammaRegularized", "[", RowBox[List[RowBox[List["1", "-", "\[Nu]"]], ",", "z"]], "]"]], RowBox[List["\[Nu]", "-", "1"]]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", "\[Nu]"]], "]"]], "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> <msub> <semantics> <mi> E </mi> <annotation encoding='Mathematica'> TagBox["E", ExpIntegralE] </annotation> </semantics> <mi> ν </mi> </msub> <mo> ( </mo> <mrow> <msup> <semantics> <mi> Q </mi> <annotation-xml encoding='MathML-Content'> <ci> GammaRegularized </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> ν </mi> </mrow> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <msup> <mrow> <msup> <semantics> <mi> Q </mi> <annotation-xml encoding='MathML-Content'> <ci> GammaRegularized </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> ν </mi> </mrow> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> ν </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> ν </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> ExpIntegralE </ci> <ci> ν </ci> <apply> <ci> InverseGammaRegularized </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <ci> InverseGammaRegularized </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> </apply> <ci> z </ci> </apply> <apply> <plus /> <ci> ν </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> ν </ci> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ExpIntegralE", "[", RowBox[List["\[Nu]_", ",", RowBox[List["InverseGammaRegularized", "[", RowBox[List[RowBox[List["1", "-", "\[Nu]_"]], ",", "z_"]], "]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox[RowBox[List["InverseGammaRegularized", "[", RowBox[List[RowBox[List["1", "-", "\[Nu]"]], ",", "z"]], "]"]], RowBox[List["\[Nu]", "-", "1"]]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", "\[Nu]"]], "]"]], " ", "z"]]]]]]

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

2001-10-29