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http://functions.wolfram.com/02.06.06.0017.01
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EulerGamma == Sum[k Sum[(-1)^j/j, {j, 2^k, 2^(k + 1) - 1}], {k, 1, Infinity}]
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Cell[BoxData[RowBox[List["EulerGamma", "\[Equal]", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List["k", RowBox[List["(", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", SuperscriptBox["2", "k"]]], RowBox[List[SuperscriptBox["2", RowBox[List["k", "+", "1"]]], "-", "1"]]], FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "j"], "j"]]], ")"]]]]]]]]]]
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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> <semantics> <mi> ℽ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubledGamma]", Function[EulerGamma]] </annotation> </semantics> <mo> ⩵ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> ∞ </mi> </munderover> <mrow> <mi> k </mi> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> j </mi> <mo> = </mo> <msup> <mn> 2 </mn> <mi> k </mi> </msup> </mrow> <mrow> <msup> <mn> 2 </mn> <mrow> <mi> k </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> j </mi> </msup> <mi> j </mi> </mfrac> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <eulergamma /> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <ci> k </ci> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <apply> <power /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </lowlimit> <uplimit> <apply> <plus /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> k </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <apply> <power /> <ci> j </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "EulerGamma", "]"]], "\[RuleDelayed]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List["k", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", SuperscriptBox["2", "k"]]], RowBox[List[SuperscriptBox["2", RowBox[List["k", "+", "1"]]], "-", "1"]]], FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "j"], "j"]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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