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http://functions.wolfram.com/02.06.06.0003.01
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EulerGamma == Sum[((-1)^k/k) Floor[Log[2, k]], {k, 1, Infinity}]
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Cell[BoxData[RowBox[List["EulerGamma", "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " "]], "k"], RowBox[List["Floor", "[", RowBox[List["Log", "[", RowBox[List["2", ",", "k"]], "]"]], "]"]]]]]]]]]]
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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> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mtext> </mtext> </mrow> <mi> k </mi> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ⌊ </mo> <mrow> <msub> <mi> log </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mi> k </mi> <mo> ) </mo> </mrow> <mo> ⌋ </mo> </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 /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <power /> <ci> k </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <floor /> <apply> <log /> <logbase> <cn type='integer'> 2 </cn> </logbase> <ci> k </ci> </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]"], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["Floor", "[", RowBox[List["Log", "[", RowBox[List["2", ",", "k"]], "]"]], "]"]]]], "k"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
