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http://functions.wolfram.com/02.09.07.0002.01
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Khinchin == Exp[(1/Log[2]) Integrate[Log[Floor[t]]/(t (t + 1)),
{t, 1, Infinity}]]
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Cell[BoxData[RowBox[List["Khinchin", "\[Equal]", RowBox[List["Exp", "[", RowBox[List[FractionBox["1", RowBox[List["Log", "[", "2", "]"]]], RowBox[List[SubsuperscriptBox["\[Integral]", "1", "\[Infinity]"], RowBox[List[FractionBox[RowBox[List["Log", "[", RowBox[List["Floor", "[", "t", "]"]], "]"]], RowBox[List["t", " ", RowBox[List["(", RowBox[List["t", "+", "1"]], ")"]]]]], RowBox[List["\[DifferentialD]", "t"]]]]]]]], "]"]]]]]]
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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> K </mi> <annotation encoding='Mathematica'> TagBox["K", Function[List[], Khinchin]] </annotation> </semantics> <mo> ⩵ </mo> <mrow> <mi> exp </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <msubsup> <mo> ∫ </mo> <mn> 1 </mn> <mi> ∞ </mi> </msubsup> <mrow> <mfrac> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mo> ⌊ </mo> <mi> t </mi> <mo> ⌋ </mo> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> t </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> t </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> t </mi> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <ci> Khinchin </ci> <apply> <exp /> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <ln /> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <int /> <bvar> <ci> t </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <ln /> <apply> <floor /> <ci> t </ci> </apply> </apply> <apply> <power /> <apply> <times /> <ci> t </ci> <apply> <plus /> <ci> t </ci> <cn type='integer'> 1 </cn> </apply> </apply> <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", "[", "Khinchin", "]"]], "\[RuleDelayed]", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List[SubsuperscriptBox["\[Integral]", "1", "\[Infinity]"], RowBox[List[FractionBox[RowBox[List["Log", "[", RowBox[List["Floor", "[", "t", "]"]], "]"]], RowBox[List["t", " ", RowBox[List["(", RowBox[List["t", "+", "1"]], ")"]]]]], RowBox[List["\[DifferentialD]", "t"]]]]]], RowBox[List["Log", "[", "2", "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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