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Root






Mathematica Notation

Traditional Notation









Elementary Functions > Root[polynomialInzk] > Limit representations





http://functions.wolfram.com/01.33.09.0001.01









  


  










Input Form





Root[Function[z, Sum[Subscript[a, j] z^j, {j, 0, n}]], k] == Limit[Subscript[w, k]^m, m -> Infinity] /; Subscript[w, k]^(m + 1) == Subscript[w, k]^m - Sum[Subscript[a, j] ((Subscript[w, k]^m)^j/ Product[If[i != j, Subscript[w, i]^m - Subscript[w, j]^m, 1], {i, 1, m}, {j, 1, m}]), {j, 0, n}] && Element[Subscript[w, k]^0, Complexes] && Subscript[w, k]^0 != Subscript[w, l]^0










Standard Form





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MathML Form







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</mo> <mrow> <msubsup> <mi> w </mi> <mi> k </mi> <mi> m </mi> </msubsup> <mo> - </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mfrac> <mrow> <msub> <mi> a </mi> <mi> j </mi> </msub> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <msubsup> <mi> w </mi> <mi> k </mi> <mi> m </mi> </msubsup> <mo> ) </mo> </mrow> <mi> j </mi> </msup> </mrow> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> i </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> m </mi> </munderover> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> m </mi> </munderover> <mrow> <mi> If </mi> <mo> [ </mo> <mrow> <mrow> <mi> i </mi> <mo> &#8800; </mo> <mi> j </mi> </mrow> <mo> , </mo> <mrow> <msubsup> <mi> w </mi> <mi> i </mi> <mi> m </mi> </msubsup> <mo> - </mo> <msubsup> <mi> w </mi> <mi> j </mi> <mi> m </mi> </msubsup> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> </mrow> </mfrac> </mrow> </mrow> </mrow> <mo> &#8743; 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Rule Form





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





2001-10-29





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