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EulerPhi




Mathematica Notation

Traditional Notation









Number Theory Functions > EulerPhi[n] > Operations > Limit operation





http://functions.wolfram.com/13.06.25.0005.01









  


  








Input Form





Limit[Max[EulerPhi[EulerPhi[2]]/2, EulerPhi[EulerPhi[3]]/3, \[Ellipsis], EulerPhi[EulerPhi[n]]/n], n -> Infinity] == 1/2








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List["Max", "[", RowBox[List[FractionBox[RowBox[List["EulerPhi", "[", RowBox[List["EulerPhi", "[", "2", "]"]], "]"]], "2"], " ", ",", FractionBox[RowBox[List["EulerPhi", "[", RowBox[List["EulerPhi", "[", "3", "]"]], "]"]], "3"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List["EulerPhi", "[", RowBox[List["EulerPhi", "[", "n", "]"]], "]"]], "n"]]], "]"]], ",", RowBox[List["n", "\[Rule]", "\[Infinity]"]]]], "]"]], "\[Equal]", FractionBox["1", "2"]]]]]








MathML Form







<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> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mi> &#8734; </mi> </mrow> </munder> <mo> &#8290; </mo> <mtext> &#8201; </mtext> <mrow> <mi> max </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, EulerPhi] </annotation> </semantics> <mo> ( </mo> <mrow> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, EulerPhi] </annotation> </semantics> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, EulerPhi] </annotation> </semantics> <mo> ( </mo> <mrow> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, EulerPhi] </annotation> </semantics> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <mfrac> <mn> 1 </mn> <mi> n </mi> </mfrac> <mo> &#8290; </mo> <mrow> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, EulerPhi] </annotation> </semantics> <mo> ( </mo> <mrow> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, EulerPhi] </annotation> </semantics> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </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> <max /> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <ci> EulerPhi </ci> <apply> <ci> EulerPhi </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 3 </cn> <apply> <ci> EulerPhi </ci> <apply> <ci> EulerPhi </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <ci> &#8230; </ci> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> EulerPhi </ci> <apply> <ci> EulerPhi </ci> <ci> n </ci> </apply> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Limit", "[", RowBox[List[RowBox[List["Max", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["EulerPhi", "[", RowBox[List["EulerPhi", "[", "2", "]"]], "]"]]]], ",", RowBox[List[FractionBox["1", "3"], " ", RowBox[List["EulerPhi", "[", RowBox[List["EulerPhi", "[", "3", "]"]], "]"]]]], ",", "\[Ellipsis]_", ",", FractionBox[RowBox[List["EulerPhi", "[", RowBox[List["EulerPhi", "[", "n_", "]"]], "]"]], "n_"]]], "]"]], ",", RowBox[List["n_", "\[Rule]", "\[Infinity]"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox["1", "2"]]]]]


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





2001-10-29