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EulerGamma




Mathematica Notation

Traditional Notation









Constants > EulerGamma > Integral representations > On the real axis > Of the direct function





http://functions.wolfram.com/02.06.07.0015.01









  


  








Input Form





EulerGamma == 1 - Integrate[(1/(t + 1)) Sum[t^2^k, {k, 1, Infinity}], {t, 0, 1}]








Standard Form





Cell[BoxData[RowBox[List["EulerGamma", "\[Equal]", RowBox[List["1", "-", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "1"], RowBox[List[FractionBox["1", RowBox[List["t", "+", "1"]]], RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], SuperscriptBox["t", SuperscriptBox["2", "k"]]]], ")"]], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[EulerGamma]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <msubsup> <mo> &#8747; </mo> <mn> 0 </mn> <mn> 1 </mn> </msubsup> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mi> t </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> &#8734; </mi> </munderover> <mrow> <msup> <mi> t </mi> <msup> <mn> 2 </mn> <mi> k </mi> </msup> </msup> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> t </mi> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[EulerGamma]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <msubsup> <mo> &#8747; </mo> <mn> 0 </mn> <mn> 1 </mn> </msubsup> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mi> t </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> &#8734; </mi> </munderover> <mrow> <msup> <mi> t </mi> <msup> <mn> 2 </mn> <mi> k </mi> </msup> </msup> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> t </mi> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "EulerGamma", "]"]], "\[RuleDelayed]", RowBox[List["1", "-", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "1"], RowBox[List[FractionBox[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], SuperscriptBox["t", SuperscriptBox["2", "k"]]]], RowBox[List["t", "+", "1"]]], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]]]]


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





2001-10-29