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MoebiusMu




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/13.07.23.0012.01









  


  








Input Form





Sum[KroneckerDelta[MoebiusMu[k] + 1]/k^2, {k, 1, n}] == 9/(2 Pi^2)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "n"], FractionBox[RowBox[List["KroneckerDelta", "[", RowBox[List[RowBox[List["MoebiusMu", "[", "k", "]"]], "+", "1"]], "]"]], SuperscriptBox["k", "2"]]]], "\[Equal]", FractionBox["9", RowBox[List["2", 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> n </mi> </munderover> <mfrac> <msub> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> KroneckerDelta </ci> </annotation-xml> </semantics> <mrow> <mrow> <semantics> <mi> &#956; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Mu]&quot;, MoebiusMu] </annotation> </semantics> <mo> ( </mo> <mi> k </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <msup> <mi> k </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> <mo> &#10869; </mo> <mfrac> <mn> 9 </mn> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <ci> KroneckerDelta </ci> <apply> <plus /> <apply> <ci> MoebiusMu </ci> <ci> k </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <power /> <ci> k </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> </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"]], "n_"], FractionBox[RowBox[List["KroneckerDelta", "[", RowBox[List[RowBox[List["MoebiusMu", "[", "k", "]"]], "+", "1"]], "]"]], SuperscriptBox["k", "2"]]]], "]"]], "\[RuleDelayed]", FractionBox["9", RowBox[List["2", " ", SuperscriptBox["\[Pi]", "2"]]]]]]]]










Contributed by





Ed Pegg


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





2007-05-02