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http://functions.wolfram.com/02.06.07.0009.01
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EulerGamma == ((\[Alpha] \[Beta])/(\[Alpha] - \[Beta]))
Integrate[(E^(-t^\[Alpha]) - E^(-t^\[Beta]))/t, {t, 0, Infinity}] /;
\[Alpha] > 0 && \[Beta] > 0
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Cell[BoxData[RowBox[List[RowBox[List["EulerGamma", "\[Equal]", RowBox[List[FractionBox[RowBox[List["\[Alpha]", " ", "\[Beta]"]], RowBox[List["\[Alpha]", "-", "\[Beta]"]]], " ", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", SuperscriptBox["t", "\[Alpha]"]]]], "-", SuperscriptBox["\[ExponentialE]", RowBox[List["-", SuperscriptBox["t", "\[Beta]"]]]]]], "t"], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]], "/;", RowBox[List[RowBox[List["\[Alpha]", ">", "0"]], "\[And]", RowBox[List["\[Beta]", ">", "0"]]]]]]]]
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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> <semantics> <mi> ℽ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubledGamma]", Function[EulerGamma]] </annotation> </semantics> <mo> ⩵ </mo> <mrow> <mfrac> <mrow> <mi> α </mi> <mo> ⁢ </mo> <mi> β </mi> </mrow> <mrow> <mi> α </mi> <mo> - </mo> <mi> β </mi> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <msubsup> <mo> ∫ </mo> <mn> 0 </mn> <mi> ∞ </mi> </msubsup> <mrow> <mfrac> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mo> - </mo> <msup> <mi> t </mi> <mi> α </mi> </msup> </mrow> </msup> <mo> - </mo> <msup> <mi> ⅇ </mi> <mrow> <mo> - </mo> <msup> <mi> t </mi> <mi> β </mi> </msup> </mrow> </msup> </mrow> <mi> t </mi> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> t </mi> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> α </mi> <mo> > </mo> <mn> 0 </mn> </mrow> <mo> ∧ </mo> <mrow> <mi> β </mi> <mo> > </mo> <mn> 0 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <eulergamma /> <apply> <times /> <apply> <times /> <ci> α </ci> <ci> β </ci> <apply> <power /> <apply> <plus /> <ci> α </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> β </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <int /> <bvar> <ci> t </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <plus /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> t </ci> <ci> α </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> t </ci> <ci> β </ci> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> t </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <gt /> <ci> α </ci> <cn type='integer'> 0 </cn> </apply> <apply> <gt /> <ci> β </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "EulerGamma", "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["\[Alpha]", " ", "\[Beta]"]], ")"]], " ", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", SuperscriptBox["t", "\[Alpha]"]]]], "-", SuperscriptBox["\[ExponentialE]", RowBox[List["-", SuperscriptBox["t", "\[Beta]"]]]]]], "t"], RowBox[List["\[DifferentialD]", "t"]]]]]]]], RowBox[List["\[Alpha]", "-", "\[Beta]"]]], "/;", RowBox[List[RowBox[List["\[Alpha]", ">", "0"]], "&&", RowBox[List["\[Beta]", ">", "0"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
