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Multinomial






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Multinomial[n1,n2,...,nm] > Summation > Finite summation





http://functions.wolfram.com/06.04.23.0002.01









  


  










Input Form





BoxData[\(\(\(Sum[\(\(\(\((\(-1\))\)^\((\(Sum[\(\(Subscript[\(k, h\)]\), \({h, 10, n}\)\)]\) -\ \(\ \ \ \ \ \ \ \ \)\(Sum[\(\(Subscript[\(σ, h\)]\), \({h, 1, \(n - 1\)}\)\)]\))\)\) * \(Multinomial[\(\(\(Subscript[\(σ, n\)]\) - \(Subscript[\(k, n\)]\)\), \(\(Subscript[\(k, n\)]\) - \(Subscript[\(σ, \(n - 1\)\)]\)\), \(\(Subscript[\(σ, \(n - 1\)\)]\) - \(Subscript[\(k, \(n - 1\)\)]\)\), \(\(Subscript[\(k, \(n - 1\)\)]\) - \(Subscript[\(σ, \(n - 2\)\)]\)\), …, \(\(Subscript[\(σ, \(q + 2\)\)]\) - \(Subscript[\(k, \(q + 2\)\)]\)\), \(\(Subscript[\(k, \(q + 2\)\)]\) - \(Subscript[\(σ, \(q + 1\)\)]\)\), \(\(Subscript[\(σ, \(q + 1\)\)]\) - \(Subscript[\(k, q\)]\)\), \(Subscript[\(σ, q\)]\)\)]\) * \(Multinomial[\(\(\(Subscript[\(σ, q\)]\) - \(Subscript[\(k, q\)]\)\), \(\(Subscript[\(k, q\)]\) - \(Subscript[\(σ, \(q - 1\)\)]\)\), \(\(Subscript[\(σ, \(q - 1\)\)]\) - \(Subscript[\(k, \(q - 1\)\)]\)\), \(\(Subscript[\(k, \(q - 1\)\)]\) - \(Subscript[\(σ, \(q - 2\)\)]\)\), …, \(\(Subscript[\(σ, 2\)]\) - \(Subscript[\(k, 2\)]\)\), \(\(Subscript[\(k, 2\)]\) - \(Subscript[\(σ, 1\)]\)\), \(\(Subscript[\(σ, 1\)]\) - \(Subscript[\(k, 0\)]\)\), \(Subscript[\(σ, 0\)]\)\)]\)\), \({\(Subscript[\(j, 1\)]\), \(Subscript[\(σ, 0\)]\), \(Subscript[\(σ, 1\)]\)}\), \({\(Subscript[\(j, 2\)]\), \(Subscript[\(σ, 1\)]\), \(Subscript[\(σ, 2\)]\)}\), …, \({\(Subscript[\(j, n\)]\), \(Subscript[\(σ, \(n - 1\)\)]\), \(Subscript[\(σ, n\)]\)}\)\)]\)  \(Product[\(\(KroneckerDelta[\(\(Subscript[\(σ, \(j - 1\)\)]\), \(Subscript[\(σ, j\)]\)\)]\), \({j, 1, n}\)\)]\)\)/;\ \(\(\(Subscript[\(σ, 0\)]\) ∈ Integers\) && \(\(Subscript[\(σ, 0\)]\) ≥ 0\) && \(\(Subscript[\(σ, 1\)]\) ∈ Integers\) && \(\(Subscript[\(σ, 1\)]\) ≥ 0\) && … && \(\(Subscript[\(σ, n\)]\) ∈ Integers\) && \(\(Subscript[\(σ, n\)]\) ≥ 0\) && \(\(Subscript[\(σ, 0\)]\) ≤ \(Subscript[\(σ, 1\)]\) ≤ … ≤ \(Subscript[\(σ, \(n - 1\)\)]\) ≤ \(Subscript[\(σ, n\)]\)\) && \(q ∈ Integers\) && \(0 ≤ q ≤ n\) && \(n ∈ Integers\) && \(n ≥ 1\)\)\)]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["j", "1"], "=", SubscriptBox["\[Sigma]", "0"]]], SubscriptBox["\[Sigma]", "1"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["j", "2"], "=", SubscriptBox["\[Sigma]", "1"]]], SubscriptBox["\[Sigma]", "2"]], RowBox[List["\[Ellipsis]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["j", "n"], "=", SubscriptBox["\[Sigma]", RowBox[List["n", "-", "1"]]]]], SubscriptBox["\[Sigma]", "n"]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "10"]], "n"], SubscriptBox["k", "h"]]], "-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["h", "=", "1"]], RowBox[List["n", "-", "1"]]], SubscriptBox["\[Sigma]", "h"]]]]]], RowBox[List["Multinomial", "[", RowBox[List[RowBox[List[SubscriptBox["\[Sigma]", "n"], "-", SubscriptBox["k", "n"]]], ",", RowBox[List[SubscriptBox["k", "n"], "-", SubscriptBox["\[Sigma]", RowBox[List["n", "-", "1"]]]]], ",", RowBox[List[SubscriptBox["\[Sigma]", RowBox[List["n", "-", "1"]]], "-", SubscriptBox["k", RowBox[List["n", "-", "1"]]]]], ",", RowBox[List[SubscriptBox["k", RowBox[List["n", "-", "1"]]], "-", SubscriptBox["\[Sigma]", RowBox[List["n", "-", "2"]]]]], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["\[Sigma]", RowBox[List["q", "+", "2"]]], "-", SubscriptBox["k", RowBox[List["q", "+", "2"]]]]], ",", RowBox[List[SubscriptBox["k", RowBox[List["q", "+", "2"]]], "-", SubscriptBox["\[Sigma]", RowBox[List["q", "+", "1"]]]]], ",", RowBox[List[SubscriptBox["\[Sigma]", RowBox[List["q", "+", "1"]]], "-", SubscriptBox["k", "q"]]], ",", SubscriptBox["\[Sigma]", "q"]]], "]"]], RowBox[List["Multinomial", "[", RowBox[List[RowBox[List[SubscriptBox["\[Sigma]", "q"], "-", SubscriptBox["k", "q"]]], ",", RowBox[List[SubscriptBox["k", "q"], "-", SubscriptBox["\[Sigma]", RowBox[List["q", "-", "1"]]]]], ",", RowBox[List[SubscriptBox["\[Sigma]", RowBox[List["q", "-", "1"]]], "-", SubscriptBox["k", RowBox[List["q", "-", "1"]]]]], ",", RowBox[List[SubscriptBox["k", RowBox[List["q", "-", "1"]]], "-", SubscriptBox["\[Sigma]", RowBox[List["q", "-", "2"]]]]], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["\[Sigma]", "2"], "-", SubscriptBox["k", "2"]]], ",", RowBox[List[SubscriptBox["k", "2"], "-", SubscriptBox["\[Sigma]", "1"]]], ",", RowBox[List[SubscriptBox["\[Sigma]", "1"], "-", SubscriptBox["k", "0"]]], ",", SubscriptBox["\[Sigma]", "0"]]], "]"]]]]]]]]]]]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "n"], RowBox[List["KroneckerDelta", "[", RowBox[List[SubscriptBox["\[Sigma]", RowBox[List["j", "-", "1"]]], ",", SubscriptBox["\[Sigma]", "j"]]], "]"]]]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["\[Sigma]", "0"], "\[Element]", "Integers"]], "\[And]", RowBox[List[SubscriptBox["\[Sigma]", "0"], "\[GreaterEqual]", "0"]], "\[And]", RowBox[List[SubscriptBox["\[Sigma]", "1"], "\[Element]", "Integers"]], "\[And]", RowBox[List[SubscriptBox["\[Sigma]", "1"], "\[GreaterEqual]", "0"]], "\[And]", "\[Ellipsis]", "\[And]", RowBox[List[SubscriptBox["\[Sigma]", "n"], "\[Element]", "Integers"]], "\[And]", RowBox[List[SubscriptBox["\[Sigma]", "n"], "\[GreaterEqual]", "0"]], "\[And]", RowBox[List[SubscriptBox["\[Sigma]", "0"], "\[LessEqual]", SubscriptBox["\[Sigma]", "1"], "\[LessEqual]", "\[Ellipsis]", "\[LessEqual]", SubscriptBox["\[Sigma]", RowBox[List["n", "-", "1"]]], "\[LessEqual]", SubscriptBox["\[Sigma]", "n"]]], "\[And]", RowBox[List["q", "\[Element]", "Integers"]], "\[And]", RowBox[List["0", "\[LessEqual]", "q", "\[LessEqual]", "n"]], "\[And]", RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "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> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> = </mo> <msub> <mi> &#963; </mi> <mn> 0 </mn> </msub> </mrow> <msub> <mi> &#963; </mi> <mn> 1 </mn> </msub> </munderover> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> = </mo> <msub> <mi> &#963; </mi> <mn> 1 </mn> </msub> </mrow> <msub> <mi> &#963; </mi> <mn> 2 </mn> </msub> </munderover> <mrow> <mo> &#8230; </mo> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mi> j </mi> <mi> n </mi> </msub> <mo> = </mo> <msub> <mi> &#963; </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <msub> <mi> &#963; </mi> <mi> n </mi> </msub> </munderover> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> h </mi> <mo> = </mo> <mn> 10 </mn> </mrow> <mi> n </mi> </munderover> <msub> <mi> k </mi> <mi> h </mi> </msub> </mrow> <mo> - </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> h </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <msub> <mi> &#963; </mi> <mi> h </mi> </msub> </mrow> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> &#963; </mi> <mi> n </mi> </msub> <mo> ; </mo> <mrow> <msub> <mi> &#963; </mi> <mi> n </mi> </msub> <mo> - </mo> <msub> <mi> k </mi> <mi> n </mi> </msub> </mrow> </mrow> <mo> , </mo> <mrow> <msub> <mi> k </mi> <mi> n </mi> </msub> <mo> - </mo> <msub> <mi> &#963; </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> , </mo> <mrow> <msub> <mi> &#963; </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> - </mo> <msub> <mi> k </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> , </mo> <mrow> <msub> <mi> k </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> - </mo> <msub> <mi> &#963; </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </msub> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <msub> <mi> &#963; </mi> <mrow> <mi> q </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </msub> <mo> - </mo> <msub> <mi> k </mi> <mrow> <mi> q </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </msub> </mrow> <mo> , </mo> <mrow> <msub> <mi> k </mi> <mrow> <mi> q </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </msub> <mo> - </mo> <msub> <mi> &#963; </mi> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> , </mo> <mrow> <msub> <mi> &#963; </mi> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> - </mo> <msub> <mi> k </mi> <mi> q </mi> </msub> </mrow> <mo> , </mo> <msub> <mi> &#963; </mi> <mi> q </mi> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> &#963; </mi> <mi> q </mi> </msub> <mo> ; </mo> <mrow> <msub> <mi> &#963; </mi> <mi> q </mi> </msub> <mo> - </mo> <msub> <mi> k </mi> <mi> q </mi> </msub> </mrow> </mrow> <mo> , </mo> <mrow> <msub> <mi> k </mi> <mi> q </mi> </msub> <mo> - </mo> <msub> <mi> &#963; </mi> <mrow> <mi> q </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> , </mo> <mrow> <msub> <mi> &#963; </mi> <mrow> <mi> q </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> - </mo> <msub> <mi> k </mi> <mrow> <mi> q </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> , </mo> <mrow> <msub> <mi> k </mi> <mrow> <mi> q </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> - </mo> <msub> <mi> &#963; </mi> <mrow> <mi> q </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </msub> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <msub> <mi> &#963; </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> k </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <mrow> <msub> <mi> k </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> &#963; </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mrow> <msub> <mi> &#963; </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> k </mi> <mn> 0 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> &#963; </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <msub> <mi> &#948; </mi> <mrow> <msub> <mi> &#963; </mi> <mrow> <mi> j </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <msub> <mi> &#963; </mi> <mi> j </mi> </msub> </mrow> </msub> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> &#963; </mi> <mn> 0 </mn> </msub> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> &#963; </mi> <mn> 1 </mn> </msub> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> <mo> &#8743; </mo> <mo> &#8230; </mo> <mo> &#8743; </mo> <mrow> <msub> <mi> &#963; </mi> <mi> n </mi> </msub> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> &#963; </mi> <mn> 0 </mn> </msub> <mo> &#8804; </mo> <msub> <mi> &#963; </mi> <mn> 1 </mn> </msub> <mo> &#8804; </mo> <mo> &#8230; </mo> <mo> &#8804; </mo> <msub> <mi> &#963; </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> &#8804; </mo> <msub> <mi> &#963; </mi> <mi> n </mi> </msub> </mrow> <mo> &#8743; </mo> <mrow> <mi> q </mi> <mo> &#8712; </mo> </mrow> <mo> &#8743; </mo> <mi> &#8469; </mi> <mo> &#8743; </mo> <mtext> </mtext> <mrow> <mn> 0 </mn> <mo> &#8804; </mo> <mi> q </mi> <mo> &#8804; </mo> <mi> n </mi> </mrow> <mo> &#8743; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> = </mo> <msub> <mi> &#963; </mi> <mn> 0 </mn> </msub> </mrow> <msub> <mi> &#963; </mi> <mn> 1 </mn> </msub> </munderover> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> = </mo> <msub> <mi> &#963; </mi> <mn> 1 </mn> </msub> </mrow> <msub> <mi> &#963; </mi> <mn> 2 </mn> </msub> </munderover> <mrow> <mo> &#8230; </mo> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mi> j </mi> <mi> n </mi> </msub> <mo> = </mo> <msub> <mi> &#963; </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <msub> <mi> &#963; </mi> <mi> n </mi> </msub> </munderover> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> h </mi> <mo> = </mo> <mn> 10 </mn> </mrow> <mi> n </mi> </munderover> <msub> <mi> k </mi> <mi> h </mi> </msub> </mrow> <mo> - </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> h </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <msub> <mi> &#963; </mi> <mi> h </mi> </msub> </mrow> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> &#963; </mi> <mi> n </mi> </msub> <mo> ; </mo> <mrow> <msub> <mi> &#963; </mi> <mi> n </mi> </msub> <mo> - </mo> <msub> <mi> k </mi> <mi> n </mi> </msub> </mrow> </mrow> <mo> , </mo> <mrow> <msub> <mi> k </mi> <mi> n </mi> </msub> <mo> - </mo> <msub> <mi> &#963; </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> , </mo> <mrow> <msub> <mi> &#963; </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> - </mo> <msub> <mi> k </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> , </mo> <mrow> <msub> <mi> k </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> - </mo> <msub> <mi> &#963; </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </msub> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <msub> <mi> &#963; </mi> <mrow> <mi> q </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </msub> <mo> - </mo> <msub> <mi> k </mi> <mrow> <mi> q </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </msub> </mrow> <mo> , </mo> <mrow> <msub> <mi> k </mi> <mrow> <mi> q </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </msub> <mo> - </mo> <msub> <mi> &#963; </mi> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> , </mo> <mrow> <msub> <mi> &#963; </mi> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> - </mo> <msub> <mi> k </mi> <mi> q </mi> </msub> </mrow> <mo> , </mo> <msub> <mi> &#963; </mi> <mi> q </mi> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> &#963; </mi> <mi> q </mi> </msub> <mo> ; </mo> <mrow> <msub> <mi> &#963; </mi> <mi> q </mi> </msub> <mo> - </mo> <msub> <mi> k </mi> <mi> q </mi> </msub> </mrow> </mrow> <mo> , </mo> <mrow> <msub> <mi> k </mi> <mi> q </mi> </msub> <mo> - </mo> <msub> <mi> &#963; </mi> <mrow> <mi> q </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> , </mo> <mrow> <msub> <mi> &#963; </mi> <mrow> <mi> q </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> - </mo> <msub> <mi> k </mi> <mrow> <mi> q </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> , </mo> <mrow> <msub> <mi> k </mi> <mrow> <mi> q </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> - </mo> <msub> <mi> &#963; </mi> <mrow> <mi> q </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </msub> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <msub> <mi> &#963; </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> k </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <mrow> <msub> <mi> k </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> &#963; </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mrow> <msub> <mi> &#963; </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> k </mi> <mn> 0 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> &#963; </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <msub> <mi> &#948; </mi> <mrow> <msub> <mi> &#963; </mi> <mrow> <mi> j </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <msub> <mi> &#963; </mi> <mi> j </mi> </msub> </mrow> </msub> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> &#963; </mi> <mn> 0 </mn> </msub> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> &#963; </mi> <mn> 1 </mn> </msub> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> <mo> &#8743; </mo> <mo> &#8230; </mo> <mo> &#8743; </mo> <mrow> <msub> <mi> &#963; </mi> <mi> n </mi> </msub> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> &#963; </mi> <mn> 0 </mn> </msub> <mo> &#8804; </mo> <msub> <mi> &#963; </mi> <mn> 1 </mn> </msub> <mo> &#8804; </mo> <mo> &#8230; </mo> <mo> &#8804; </mo> <msub> <mi> &#963; </mi> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> &#8804; </mo> <msub> <mi> &#963; </mi> <mi> n </mi> </msub> </mrow> <mo> &#8743; </mo> <mrow> <mi> q </mi> <mo> &#8712; </mo> </mrow> <mo> &#8743; </mo> <mi> &#8469; </mi> <mo> &#8743; </mo> <mtext> </mtext> <mrow> <mn> 0 </mn> <mo> &#8804; </mo> <mi> q </mi> <mo> &#8804; </mo> <mi> n </mi> </mrow> <mo> &#8743; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18





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