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Khinchin




Mathematica Notation

Traditional Notation









Constants > Khinchin > Primary definition





http://functions.wolfram.com/02.09.02.0001.01









  


  








Input Form





Khinchin == Product[(1 + 1/(k (k + 2)))^Log[2, k], {k, 1, Infinity}]








Standard Form





Cell[BoxData[RowBox[List["Khinchin", "\[Equal]", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "\[Infinity]"], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", FractionBox["1", RowBox[List["k", " ", RowBox[List["(", RowBox[List["k", "+", "2"]], ")"]]]]]]], ")"]], RowBox[List["Log", "[", RowBox[List["2", ",", "k"]], "]"]]]]]]]]]








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> K </mi> <annotation encoding='Mathematica'> TagBox[&quot;K&quot;, Function[List[], Khinchin]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> &#8734; </mi> </munderover> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 1 </mn> <mrow> <mi> k </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> k </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mrow> <msub> <mi> log </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mi> k </mi> <mo> ) </mo> </mrow> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <ci> Khinchin </ci> <apply> <product /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <ci> k </ci> <apply> <plus /> <ci> k </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <log /> <logbase> <cn type='integer'> 2 </cn> </logbase> <ci> k </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "Khinchin", "]"]], "\[RuleDelayed]", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "\[Infinity]"], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", FractionBox["1", RowBox[List["k", " ", RowBox[List["(", RowBox[List["k", "+", "2"]], ")"]]]]]]], ")"]], RowBox[List["Log", "[", RowBox[List["2", ",", "k"]], "]"]]]]]]]]]


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





2001-10-29