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variants of this functions
HermiteH




Mathematica Notation

Traditional Notation









Polynomials > HermiteH[n,z] > Zeros





http://functions.wolfram.com/05.01.30.0001.01









  


  








Input Form





Sum[If[k != j, 1/(Subscript[x, j] - Subscript[x, k]), 0], {k, 1, n}] == Subscript[x, j] /; HermiteH[n, Subscript[x, k]] == 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "n"], RowBox[List["If", "[", RowBox[List[RowBox[List["k", "\[NotEqual]", "j"]], ",", FractionBox["1", RowBox[List[SubscriptBox["x", "j"], "-", SubscriptBox["x", "k"]]]], ",", "0"]], "]"]]]], "\[Equal]", SubscriptBox["x", "j"]]], "/;", " ", RowBox[List[RowBox[List["HermiteH", "[", RowBox[List["n", ",", SubscriptBox["x", "k"]]], "]"]], "\[Equal]", "0"]]]]]]








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> <munderover> <mo> &#8721; </mo> <munder> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mrow> <mi> k </mi> <mo> &#8800; </mo> <mi> j </mi> </mrow> </munder> <mi> n </mi> </munderover> <mfrac> <mn> 1 </mn> <mrow> <msub> <mi> x </mi> <mi> j </mi> </msub> <mo> - </mo> <msub> <mi> x </mi> <mi> k </mi> </msub> </mrow> </mfrac> </mrow> <mo> &#10869; </mo> <msub> <mi> x </mi> <mi> j </mi> </msub> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> H </mi> <mi> n </mi> </msub> <mo> ( </mo> <msub> <mi> x </mi> <mi> k </mi> </msub> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mn> 0 </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> ErrorBox </ci> <apply> <ci> UnderoverscriptBox </ci> <ms> &#8721; </ms> <apply> <ci> UnderscriptBox </ci> <apply> <ci> RowBox </ci> <list> <ms> k </ms> <ms> = </ms> <ms> 1 </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> k </ms> <ms> &#8800; </ms> <ms> j </ms> </list> </apply> </apply> <ms> n </ms> </apply> </apply> <apply> <ci> FractionBox </ci> <ms> 1 </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> x </ms> <ms> j </ms> </apply> <ms> - </ms> <apply> <ci> SubscriptBox </ci> <ms> x </ms> <ms> k </ms> </apply> </list> </apply> </apply> </list> </apply> <ms> &#10869; </ms> <apply> <ci> SubscriptBox </ci> <ms> x </ms> <ms> j </ms> </apply> </list> </apply> <ms> /; </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> H </ms> <ms> n </ms> </apply> <ms> ( </ms> <apply> <ci> SubscriptBox </ci> <ms> x </ms> <ms> k </ms> </apply> <ms> ) </ms> </list> </apply> <ms> &#10869; </ms> <ms> 0 </ms> </list> </apply> </list> </apply> <ci> TraditionalForm </ci> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "1"]], "n_"], RowBox[List["If", "[", RowBox[List[RowBox[List["k_", "\[NotEqual]", "j_"]], ",", FractionBox["1", RowBox[List[SubscriptBox["x_", "j_"], "-", SubscriptBox["x_", "k_"]]]], ",", "0"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[SubscriptBox["xx", "j"], "/;", RowBox[List[RowBox[List["HermiteH", "[", RowBox[List["n", ",", SubscriptBox["x", "k"]]], "]"]], "\[Equal]", "0"]]]]]]]]


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





2001-10-29