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MoebiusMu




Mathematica Notation

Traditional Notation









Number Theory Functions > MoebiusMu[n] > Primary definition





http://functions.wolfram.com/13.07.02.0005.01









  


  








Input Form





MoebiusMu[n] == 0 /; Exists[Element[k, Integers], Element[n/k^2, Integers]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["MoebiusMu", "[", "n", "]"]], "\[Equal]", "0"]], "/;", RowBox[List[SubscriptBox["\[Exists]", RowBox[List["k", "\[Element]", "Integers"]]], RowBox[List[FractionBox["n", SuperscriptBox["k", "2"]], "\[Element]", "Integers"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <semantics> <mi> &#956; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Mu]&quot;, MoebiusMu] </annotation> </semantics> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <msub> <mo> &#8707; </mo> <mrow> <mi> k </mi> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </msub> <mrow> <mfrac> <mi> n </mi> <msup> <mi> k </mi> <mn> 2 </mn> </msup> </mfrac> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> MoebiusMu </ci> <ci> n </ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <exists /> <bvar> <apply> <in /> <ci> k </ci> <integers /> </apply> </bvar> <apply> <in /> <apply> <times /> <ci> n </ci> <apply> <power /> <apply> <power /> <ci> k </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["MoebiusMu", "[", "n_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[SubscriptBox["\[Exists]", RowBox[List["k", "\[Element]", "Integers"]]], RowBox[List[FractionBox["n", SuperscriptBox["k", "2"]], "\[Element]", "Integers"]]]]]]]]]]


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





2002-12-18