DiracDelta[Subscript[x, 1], Subscript[x, 2], \[Ellipsis], Subscript[x, n]] == Product[MeijerG[{{}, {}}, {{}, {}}, 1 - Subscript[x, k]], {k, 1, n}] /; Subscript[x, k] != Subscript[x, j] && k != j && Element[Subscript[x, k], Reals] && Subscript[x, k] < 2

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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> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> DiracDelta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> x </mi> <mn> 2 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> x </mi> <mi> n </mi> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 0 </mn> <mo> , </mo> <mn> 0 </mn> </mrow> <mrow> <mn> 0 </mn> <mo> , </mo> <mn> 0 </mn> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <msub> <mi> x </mi> <mi> k </mi> </msub> </mrow> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mo> &#8202; </mo> </mtd> </mtr> <mtr> <mtd> <mo> &#8202; </mo> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;0&quot;, &quot;,&quot;, &quot;0&quot;]], RowBox[List[&quot;0&quot;, &quot;,&quot;, &quot;0&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[RowBox[List[&quot;1&quot;, &quot;-&quot;, SubscriptBox[&quot;x&quot;, &quot;k&quot;]]], MeijerG, Rule[Editable, True]], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[TagBox[&quot;\[Null]&quot;, MeijerG, Rule[Editable, False]]], List[TagBox[&quot;\[Null]&quot;, MeijerG, Rule[Editable, False]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> x </mi> <mi> k </mi> </msub> <mo> &#8800; </mo> <msub> <mi> x </mi> <mi> j </mi> </msub> </mrow> <mo> &#8743; </mo> <mrow> <mi> k </mi> <mo> &#8800; </mo> <mi> j </mi> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> x </mi> <mi> k </mi> </msub> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> x </mi> <mi> k </mi> </msub> <mo> &lt; </mo> <mn> 2 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> DiracDelta </ci> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> x </ci> <ci> n </ci> </apply> </apply> <apply> <product /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <ci> MeijerG </ci> <list> <list /> <list /> </list> <list> <list /> <list /> </list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> x </ci> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <neq /> <apply> <ci> Subscript </ci> <ci> x </ci> <ci> k </ci> </apply> <apply> <ci> Subscript </ci> <ci> x </ci> <ci> j </ci> </apply> </apply> <apply> <neq /> <ci> k </ci> <ci> j </ci> </apply> <apply> <in /> <apply> <ci> Subscript </ci> <ci> x </ci> <ci> k </ci> </apply> <reals /> </apply> <apply> <lt /> <apply> <ci> Subscript </ci> <ci> x </ci> <ci> k </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2001-10-29