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http://functions.wolfram.com/01.33.02.0001.01
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(Sum[Subscript[a, j] z^j, {j, 0, n}] /;
z == Root[Function[z, Sum[Subscript[a, j] z^j, {j, 0, n}]], k]) == 0 /;
Element[k, Integers] && 1 <= k <= n
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SubscriptBox["a", "j"], " ", SuperscriptBox["z", "j"]]]]], "/;", RowBox[List["z", "\[Equal]", RowBox[List["Root", "[", RowBox[List[RowBox[List["Function", "[", RowBox[List["z", ",", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "n"], RowBox[List[SubscriptBox["a", "j"], SuperscriptBox["z", "j"]]]]]]], "]"]], ",", "k"]], "]"]]]]]], ")"]], "\[Equal]", "0"]], "/;", " ", RowBox[List[RowBox[List["k", "\[Element]", "Integers"]], " ", "\[And]", RowBox[List["1", "\[LessEqual]", "k", "\[LessEqual]", " ", "n", " "]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <msub> <mi> a </mi> <mi> j </mi> </msub> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> j </mi> </msup> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> z </mi> <mo> ⩵ </mo> <msubsup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ; </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <msub> <mi> a </mi> <mi> j </mi> </msub> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> j </mi> </msup> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> k </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mn> 1 </mn> <mo> ≤ </mo> <mi> k </mi> <mo> ≤ </mo> <mi> n </mi> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> Condition </ci> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> j </ci> </apply> <apply> <power /> <ci> z </ci> <ci> j </ci> </apply> </apply> </apply> <apply> <eq /> <ci> z </ci> <apply> <power /> <apply> <ci> Subscript </ci> <apply> <ci> CompoundExpression </ci> <ci> z </ci> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> j </ci> </apply> <apply> <power /> <ci> z </ci> <ci> j </ci> </apply> </apply> </apply> </apply> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <and /> <apply> <in /> <ci> k </ci> <integers /> </apply> <apply> <leq /> <cn type='integer'> 1 </cn> <ci> k </ci> <ci> n </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j_", "=", "0"]], "n_"], RowBox[List[SubscriptBox["a_", "j_"], " ", SuperscriptBox["z_", "j_"]]]]], "/;", RowBox[List["z_", "\[Equal]", RowBox[List["Root", "[", RowBox[List[RowBox[List["Function", "[", RowBox[List["z_", ",", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j_", "=", "0"]], "n_"], RowBox[List[SubscriptBox["a_", "j_"], " ", SuperscriptBox["z_", "j_"]]]]]]], "]"]], ",", "k_"]], "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List["k", "\[Element]", "Integers"]], "&&", RowBox[List["1", "\[LessEqual]", "k", "\[LessEqual]", "n"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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