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MoebiusMu




Mathematica Notation

Traditional Notation









Number Theory Functions > MoebiusMu[n] > Summation > Infinite summation





http://functions.wolfram.com/13.07.23.0009.01









  


  








Input Form





Sum[Abs[MoebiusMu[k]]/k^s, {k, 1, Infinity}] == 15/Pi^2








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List["Abs", "[", RowBox[List["MoebiusMu", "[", "k", "]"]], "]"]], SuperscriptBox["k", "s"]]]], "\[Equal]", FractionBox["15", SuperscriptBox["\[Pi]", "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> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> &#8734; </mi> </munderover> <mfrac> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mrow> <semantics> <mi> &#956; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Mu]&quot;, MoebiusMu] </annotation> </semantics> <mo> ( </mo> <mi> k </mi> <mo> ) </mo> </mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <msup> <mi> k </mi> <mi> s </mi> </msup> </mfrac> </mrow> <mo> &#10869; </mo> <mfrac> <mn> 15 </mn> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <abs /> <apply> <ci> MoebiusMu </ci> <ci> k </ci> </apply> </apply> <apply> <power /> <apply> <power /> <ci> k </ci> <ci> s </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <power /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List["Abs", "[", RowBox[List["MoebiusMu", "[", "k", "]"]], "]"]], SuperscriptBox["k", "s_"]]]], "]"]], "\[RuleDelayed]", FractionBox["15", SuperscriptBox["\[Pi]", "2"]]]]]]










Contributed by





Ed Pegg


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





2007-05-02