Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

Download All Introductions For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











ExpIntegralE






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > ExpIntegralE[nu,z] > Series representations > Generalized power series > Expansions at generic point nu==nu0 > For the function itself





http://functions.wolfram.com/06.34.06.0018.01









  


  










Input Form





ExpIntegralE[\[Nu], z] \[Proportional] ExpIntegralE[Subscript[\[Nu], 0], z] - (1/z) Gamma[1 - Subscript[\[Nu], 0]] (z Gamma[1 - Subscript[\[Nu], 0]] HypergeometricPFQRegularized[ {1 - Subscript[\[Nu], 0], 1 - Subscript[\[Nu], 0]}, {2 - Subscript[\[Nu], 0], 2 - Subscript[\[Nu], 0]}, -z] - z^Subscript[\[Nu], 0] (EulerGamma - HarmonicNumber[ -Subscript[\[Nu], 0]] + Log[z])) (\[Nu] - Subscript[\[Nu], 0]) + (1/(2 z)) Gamma[1 - Subscript[\[Nu], 0]] (-2 z Gamma[1 - Subscript[\[Nu], 0]]^2 HypergeometricPFQRegularized[ {1 - Subscript[\[Nu], 0], 1 - Subscript[\[Nu], 0], 1 - Subscript[\[Nu], 0]}, {2 - Subscript[\[Nu], 0], 2 - Subscript[\[Nu], 0], 2 - Subscript[\[Nu], 0]}, -z] + z^Subscript[\[Nu], 0] ((EulerGamma - HarmonicNumber[-Subscript[\[Nu], 0]] + Log[z])^2 + PolyGamma[1, 1 - Subscript[\[Nu], 0]])) (\[Nu] - Subscript[\[Nu], 0])^ 2 + O[(\[Nu] - Subscript[\[Nu], 0])^3]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["ExpIntegralE", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List["ExpIntegralE", "[", RowBox[List[SubscriptBox["\[Nu]", "0"], ",", "z"]], "]"]], "-", RowBox[List[FractionBox["1", "z"], RowBox[List["Gamma", "[", RowBox[List["1", "-", SubscriptBox["\[Nu]", "0"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["z", " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", SubscriptBox["\[Nu]", "0"]]], "]"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["\[Nu]", "0"]]], ",", RowBox[List["1", "-", SubscriptBox["\[Nu]", "0"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["2", "-", SubscriptBox["\[Nu]", "0"]]], ",", RowBox[List["2", "-", SubscriptBox["\[Nu]", "0"]]]]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["z", SubscriptBox["\[Nu]", "0"]], " ", RowBox[List["(", RowBox[List["EulerGamma", "-", RowBox[List["HarmonicNumber", "[", RowBox[List["-", SubscriptBox["\[Nu]", "0"]]], "]"]], "+", RowBox[List["Log", "[", "z", "]"]]]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["\[Nu]", "-", SubscriptBox["\[Nu]", "0"]]], ")"]]]], "+", RowBox[List[FractionBox["1", RowBox[List["2", " ", "z"]]], RowBox[List["Gamma", "[", RowBox[List["1", "-", SubscriptBox["\[Nu]", "0"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "z", " ", SuperscriptBox[RowBox[List["Gamma", "[", RowBox[List["1", "-", SubscriptBox["\[Nu]", "0"]]], "]"]], "2"], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["\[Nu]", "0"]]], ",", RowBox[List["1", "-", SubscriptBox["\[Nu]", "0"]]], ",", RowBox[List["1", "-", SubscriptBox["\[Nu]", "0"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["2", "-", SubscriptBox["\[Nu]", "0"]]], ",", RowBox[List["2", "-", SubscriptBox["\[Nu]", "0"]]], ",", RowBox[List["2", "-", SubscriptBox["\[Nu]", "0"]]]]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["z", SubscriptBox["\[Nu]", "0"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["EulerGamma", "-", RowBox[List["HarmonicNumber", "[", RowBox[List["-", SubscriptBox["\[Nu]", "0"]]], "]"]], "+", RowBox[List["Log", "[", "z", "]"]]]], ")"]], "2"], "+", RowBox[List["PolyGamma", "[", RowBox[List["1", ",", RowBox[List["1", "-", SubscriptBox["\[Nu]", "0"]]]]], "]"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[Nu]", "-", SubscriptBox["\[Nu]", "0"]]], ")"]], "2"]]], "+", RowBox[List["O", "[", SuperscriptBox[RowBox[List["(", RowBox[List["\[Nu]", "-", SubscriptBox["\[Nu]", "0"]]], ")"]], "3"], "]"]]]]]]]]










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> &#8733; </mo> <mrow> <mrow> <msub> <semantics> <mi> E </mi> <annotation encoding='Mathematica'> TagBox[&quot;E&quot;, ExpIntegralE] </annotation> </semantics> <msub> <mi> &#957; </mi> <mn> 0 </mn> </msub> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mfrac> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> &#957; </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mi> z </mi> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> &#957; </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 2 </mn> </msub> <msub> <mover> <mi> F </mi> <mo> ~ </mo> </mover> <mn> 2 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> &#957; </mi> <mn> 0 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> &#957; </mi> <mn> 0 </mn> </msub> </mrow> </mrow> <mo> ; </mo> <mrow> <mrow> <mn> 2 </mn> <mo> - </mo> <msub> <mi> &#957; </mi> <mn> 0 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 2 </mn> <mo> - </mo> <msub> <mi> &#957; </mi> <mn> 0 </mn> </msub> </mrow> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[&quot;2&quot;, TraditionalForm]], SubscriptBox[OverscriptBox[&quot;F&quot;, &quot;~&quot;], FormBox[&quot;2&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;\[Nu]&quot;, &quot;0&quot;]]], HypergeometricPFQRegularized, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;\[Nu]&quot;, &quot;0&quot;]]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], &quot;;&quot;, TagBox[TagBox[RowBox[List[TagBox[RowBox[List[&quot;2&quot;, &quot;-&quot;, SubscriptBox[&quot;\[Nu]&quot;, &quot;0&quot;]]], HypergeometricPFQRegularized, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;2&quot;, &quot;-&quot;, SubscriptBox[&quot;\[Nu]&quot;, &quot;0&quot;]]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], &quot;;&quot;, TagBox[RowBox[List[&quot;-&quot;, &quot;z&quot;]], HypergeometricPFQRegularized, Rule[Editable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQRegularized] </annotation> </semantics> </mrow> <mo> - </mo> <mrow> <msup> <mi> z </mi> <msub> <mi> &#957; </mi> <mn> 0 </mn> </msub> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msub> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <msub> <mi> &#957; </mi> <mn> 0 </mn> </msub> </mrow> </msub> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[EulerGamma]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> - </mo> <msub> <mi> &#957; </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> &#957; </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mtext> </mtext> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> z </mi> <msub> <mi> &#957; </mi> <mn> 0 </mn> </msub> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msub> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> HarmonicNumber </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <msub> <mi> &#957; </mi> <mn> 0 </mn> </msub> </mrow> </msub> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[EulerGamma]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <msup> <semantics> <mi> &#968; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Psi]&quot;, PolyGamma] </annotation> </semantics> <mrow> <mo> ( </mo> <mn> 1 </mn> <mo> ) </mo> </mrow> </msup> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> &#957; </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <msup> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> &#957; </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 3 </mn> </msub> <msub> <mover> <mi> F </mi> <mo> ~ </mo> </mover> <mn> 3 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> &#957; </mi> <mn> 0 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> &#957; </mi> <mn> 0 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> &#957; </mi> <mn> 0 </mn> </msub> </mrow> </mrow> <mo> ; </mo> <mrow> <mrow> <mn> 2 </mn> <mo> - </mo> <msub> <mi> &#957; </mi> <mn> 0 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 2 </mn> <mo> - </mo> <msub> <mi> &#957; </mi> <mn> 0 </mn> </msub> </mrow> <mo> , </mo> <mrow> <mn> 2 </mn> <mo> - </mo> <msub> <mi> &#957; </mi> <mn> 0 </mn> </msub> </mrow> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[&quot;3&quot;, TraditionalForm]], SubscriptBox[OverscriptBox[&quot;F&quot;, &quot;~&quot;], FormBox[&quot;3&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;\[Nu]&quot;, &quot;0&quot;]]], HypergeometricPFQRegularized, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;\[Nu]&quot;, &quot;0&quot;]]], HypergeometricPFQRegularized, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;\[Nu]&quot;, &quot;0&quot;]]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], &quot;;&quot;, TagBox[TagBox[RowBox[List[TagBox[RowBox[List[&quot;2&quot;, &quot;-&quot;, SubscriptBox[&quot;\[Nu]&quot;, &quot;0&quot;]]], HypergeometricPFQRegularized, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;2&quot;, &quot;-&quot;, SubscriptBox[&quot;\[Nu]&quot;, &quot;0&quot;]]], HypergeometricPFQRegularized, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;2&quot;, &quot;-&quot;, SubscriptBox[&quot;\[Nu]&quot;, &quot;0&quot;]]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], &quot;;&quot;, TagBox[RowBox[List[&quot;-&quot;, &quot;z&quot;]], HypergeometricPFQRegularized, Rule[Editable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQRegularized] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> - </mo> <msub> <mi> &#957; </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> - </mo> <msub> <mi> &#957; </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <ci> ExpIntegralE </ci> <ci> &#957; </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <ci> ExpIntegralE </ci> <apply> <ci> Subscript </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <ci> Gamma </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <apply> <ci> HypergeometricPFQRegularized </ci> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </list> <list> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <apply> <ci> Subscript </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> HarmonicNumber </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <apply> <ln /> <ci> z </ci> </apply> <eulergamma /> </apply> </apply> </apply> </apply> <apply> <plus /> <ci> &#957; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <apply> <ci> Subscript </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <plus /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> HarmonicNumber </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <apply> <ln /> <ci> z </ci> </apply> <eulergamma /> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> PolyGamma </ci> <cn type='integer'> 1 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> HypergeometricPFQRegularized </ci> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </list> <list> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> &#957; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> O </ci> <apply> <power /> <apply> <plus /> <ci> &#957; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ExpIntegralE", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ExpIntegralE", "[", RowBox[List[SubscriptBox["\[Nu]\[Nu]", "0"], ",", "z"]], "]"]], "-", FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["1", "-", SubscriptBox["\[Nu]\[Nu]", "0"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["z", " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", SubscriptBox["\[Nu]\[Nu]", "0"]]], "]"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["\[Nu]\[Nu]", "0"]]], ",", RowBox[List["1", "-", SubscriptBox["\[Nu]\[Nu]", "0"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["2", "-", SubscriptBox["\[Nu]\[Nu]", "0"]]], ",", RowBox[List["2", "-", SubscriptBox["\[Nu]\[Nu]", "0"]]]]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["z", SubscriptBox["\[Nu]\[Nu]", "0"]], " ", RowBox[List["(", RowBox[List["EulerGamma", "-", RowBox[List["HarmonicNumber", "[", RowBox[List["-", SubscriptBox["\[Nu]\[Nu]", "0"]]], "]"]], "+", RowBox[List["Log", "[", "z", "]"]]]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["\[Nu]", "-", SubscriptBox["\[Nu]\[Nu]", "0"]]], ")"]]]], "z"], "+", FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["1", "-", SubscriptBox["\[Nu]\[Nu]", "0"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "z", " ", SuperscriptBox[RowBox[List["Gamma", "[", RowBox[List["1", "-", SubscriptBox["\[Nu]\[Nu]", "0"]]], "]"]], "2"], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["\[Nu]\[Nu]", "0"]]], ",", RowBox[List["1", "-", SubscriptBox["\[Nu]\[Nu]", "0"]]], ",", RowBox[List["1", "-", SubscriptBox["\[Nu]\[Nu]", "0"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["2", "-", SubscriptBox["\[Nu]\[Nu]", "0"]]], ",", RowBox[List["2", "-", SubscriptBox["\[Nu]\[Nu]", "0"]]], ",", RowBox[List["2", "-", SubscriptBox["\[Nu]\[Nu]", "0"]]]]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["z", SubscriptBox["\[Nu]\[Nu]", "0"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["EulerGamma", "-", RowBox[List["HarmonicNumber", "[", RowBox[List["-", SubscriptBox["\[Nu]\[Nu]", "0"]]], "]"]], "+", RowBox[List["Log", "[", "z", "]"]]]], ")"]], "2"], "+", RowBox[List["PolyGamma", "[", RowBox[List["1", ",", RowBox[List["1", "-", SubscriptBox["\[Nu]\[Nu]", "0"]]]]], "]"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[Nu]", "-", SubscriptBox["\[Nu]\[Nu]", "0"]]], ")"]], "2"]]], RowBox[List["2", " ", "z"]]], "+", SuperscriptBox[RowBox[List["O", "[", RowBox[List["\[Nu]", "-", SubscriptBox["\[Nu]\[Nu]", "0"]]], "]"]], "3"]]]]]]]










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





2007-05-02





© 1998-2014 Wolfram Research, Inc.