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MoebiusMu




Mathematica Notation

Traditional Notation









Number Theory Functions > MoebiusMu[n] > Specific values > Specialized values





http://functions.wolfram.com/13.07.03.0001.01









  


  








Input Form





MoebiusMu[m n] == MoebiusMu[n] MoebiusMu[m] /; GCD[m, n] == 1








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["MoebiusMu", "[", RowBox[List["m", " ", "n"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["MoebiusMu", "[", "n", "]"]], RowBox[List["MoebiusMu", "[", "m", "]"]]]]]], "/;", RowBox[List[RowBox[List["GCD", "[", RowBox[List["m", ",", "n"]], "]"]], "\[Equal]", "1"]]]]]]








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> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <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> &#8290; </mo> <mrow> <semantics> <mi> &#956; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Mu]&quot;, MoebiusMu] </annotation> </semantics> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> gcd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> m </mi> <mo> , </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mn> 1 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> MoebiusMu </ci> <apply> <times /> <ci> m </ci> <ci> n </ci> </apply> </apply> <apply> <times /> <apply> <ci> MoebiusMu </ci> <ci> n </ci> </apply> <apply> <ci> MoebiusMu </ci> <ci> m </ci> </apply> </apply> </apply> <apply> <eq /> <apply> <gcd /> <ci> m </ci> <ci> n </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["MoebiusMu", "[", RowBox[List["m_", " ", "n_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["MoebiusMu", "[", "n", "]"]], " ", RowBox[List["MoebiusMu", "[", "m", "]"]]]], "/;", RowBox[List[RowBox[List["GCD", "[", RowBox[List["m", ",", "n"]], "]"]], "\[Equal]", "1"]]]]]]]]


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





2001-10-29