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http://functions.wolfram.com/13.06.25.0007.01
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Limit[Min[Subscript[{EulerPhi[n]/(n/Log[Log[n]])}, k, 1, n]],
n -> Infinity] == E^(-EulerGamma)
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Cell[BoxData[RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List["Min", "[", SubscriptBox[RowBox[List["{", FractionBox[RowBox[List["EulerPhi", "[", "n", "]"]], FractionBox["n", RowBox[List["Log", "[", RowBox[List["Log", "[", "n", "]"]], "]"]]]], "}"]], RowBox[List["k", ",", "1", ",", "n"]]], "]"]], ",", RowBox[List["n", "\[Rule]", "\[Infinity]"]]]], "]"]], "\[Equal]", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "EulerGamma"]]]]]]]
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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> <mrow> <munder> <mi> lim </mi> <mrow> <mi> n </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mi> ∞ </mi> </mrow> </munder> <mo> ⁢ </mo> <mtext>   </mtext> <mrow> <mi> min </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mrow> <mo> { </mo> <mfrac> <mrow> <semantics> <mi> ϕ </mi> <annotation encoding='Mathematica'> TagBox["\[Phi]", EulerPhi] </annotation> </semantics> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mfrac> <mi> n </mi> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mfrac> </mfrac> <mo> } </mo> </mrow> <mrow> <mi> k </mi> <mo> , </mo> <mn> 1 </mn> <mo> , </mo> <mi> n </mi> </mrow> </msub> <mo> ) </mo> </mrow> </mrow> <mo> ⩵ </mo> <msup> <mi> ⅇ </mi> <mrow> <mo> - </mo> <semantics> <mi> ℽ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubledGamma]", Function[EulerGamma]] </annotation> </semantics> </mrow> </msup> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <limit /> <bvar> <ci> n </ci> </bvar> <condition> <apply> <tendsto /> <ci> n </ci> <infinity /> </apply> </condition> <apply> <min /> <apply> <ci> Subscript </ci> <list> <apply> <times /> <apply> <ci> EulerPhi </ci> <ci> n </ci> </apply> <apply> <power /> <apply> <times /> <ci> n </ci> <apply> <power /> <apply> <ln /> <apply> <ln /> <ci> n </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </list> <ci> k </ci> <cn type='integer'> 1 </cn> <ci> n </ci> </apply> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <eulergamma /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Limit", "[", RowBox[List[RowBox[List["Min", "[", SubscriptBox[RowBox[List["{", FractionBox[RowBox[List["EulerPhi", "[", "n_", "]"]], FractionBox["n_", RowBox[List["Log", "[", RowBox[List["Log", "[", "n_", "]"]], "]"]]]], "}"]], RowBox[List["k", ",", "1", ",", "n_"]]], "]"]], ",", RowBox[List["n_", "\[Rule]", "\[Infinity]"]]]], "]"]], "]"]], "\[RuleDelayed]", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "EulerGamma"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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