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Cyclotomic




Mathematica Notation

Traditional Notation









Polynomials > Cyclotomic[n,z] > Product representations





http://functions.wolfram.com/05.11.08.0001.01









  


  








Input Form





Cyclotomic[n, z] == DivisorProduct[(1 - z^d)^MoebiusMu[n/d], {d, n}] /; n > 1








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Cyclotomic", "[", RowBox[List["n", ",", "z"]], "]"]], "\[Equal]", RowBox[List["DivisorProduct", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["z", "d"]]], ")"]], RowBox[List["MoebiusMu", "[", FractionBox["n", "d"], "]"]]], ",", RowBox[List["{", RowBox[List["d", ",", "n"]], "}"]]]], "]"]]]], "/;", RowBox[List["n", ">", "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> <msub> <semantics> <mi> C </mi> <annotation encoding='Mathematica'> TagBox[&quot;C&quot;, Cyclotomic] </annotation> </semantics> <mi> n </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mstyle scriptlevel='0'> <mrow> <mstyle minsize='2.4'> <munder> <mo> &#8719; </mo> <mrow> <mi> d </mi> <mo> &#8739; </mo> <mi> n </mi> </mrow> </munder> </mstyle> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> z </mi> <mi> d </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <semantics> <mi> &#956; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Mu]&quot;, MoebiusMu] </annotation> </semantics> <mo> ( </mo> <mfrac> <mi> n </mi> <mi> d </mi> </mfrac> <mo> ) </mo> </mrow> </msup> </mrow> </mstyle> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &gt; </mo> <mn> 1 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> FormBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <apply> <ci> TagBox </ci> <ms> C </ms> <ci> Cyclotomic </ci> </apply> <ms> n </ms> </apply> <ms> ( </ms> <ms> z </ms> <ms> ) </ms> </list> </apply> <ms> &#10869; </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> UnderscriptBox </ci> <apply> <ci> ErrorBox </ci> <ms> &#8719; </ms> </apply> <apply> <ci> RowBox </ci> <list> <ms> d </ms> <ms> &#8739; </ms> <ms> n </ms> </list> </apply> </apply> <apply> <ci> SuperscriptBox </ci> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> - </ms> <apply> <ci> SuperscriptBox </ci> <ms> z </ms> <ms> d </ms> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> TagBox </ci> <ms> &#956; </ms> <ci> MoebiusMu </ci> </apply> <ms> ( </ms> <apply> <ci> FractionBox </ci> <ms> n </ms> <ms> d </ms> </apply> <ms> ) </ms> </list> </apply> </apply> </list> </apply> </list> </apply> <ms> /; </ms> <apply> <ci> RowBox </ci> <list> <ms> n </ms> <ms> &gt; </ms> <ms> 1 </ms> </list> </apply> </list> </apply> <ci> TraditionalForm </ci> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Cyclotomic", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["DivisorProduct", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["z", "d"]]], ")"]], RowBox[List["MoebiusMu", "[", FractionBox["n", "d"], "]"]]], ",", RowBox[List["{", RowBox[List["d", ",", "n"]], "}"]]]], "]"]], "/;", RowBox[List["n", ">", "1"]]]]]]]]


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





2001-10-29