KroneckerDelta[Subscript[n, 1], Subscript[n, 2], \[Ellipsis], Subscript[n, m]] KroneckerDelta[Subscript[n, m + 1], Subscript[n, m + 2], \[Ellipsis], Subscript[n, m + r]] == KroneckerDelta[Subscript[n, 1], Subscript[n, 2], \[Ellipsis], Subscript[n, m], Subscript[n, m + 1], Subscript[n, m + 2], \[Ellipsis], Subscript[n, m + r]] /; m >= 2 && r >= 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> <msub> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> KroneckerDelta </ci> </annotation-xml> </semantics> <mrow> <msub> <mi> n </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> n </mi> <mn> 2 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> n </mi> <mi> m </mi> </msub> </mrow> </msub> <mo> &#8290; </mo> <msub> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> KroneckerDelta </ci> </annotation-xml> </semantics> <mrow> <msub> <mi> n </mi> <mrow> <mi> m </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <msub> <mi> n </mi> <mrow> <mi> m </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> n </mi> <mrow> <mi> m </mi> <mo> + </mo> <mi> r </mi> </mrow> </msub> </mrow> </msub> </mrow> <mo> &#10869; </mo> <msub> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> KroneckerDelta </ci> </annotation-xml> </semantics> <mrow> <msub> <mi> n </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> n </mi> <mn> 2 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> n </mi> <mi> m </mi> </msub> <mo> , </mo> <msub> <mi> n </mi> <mrow> <mi> m </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <msub> <mi> n </mi> <mrow> <mi> m </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> n </mi> <mrow> <mi> m </mi> <mo> + </mo> <mi> r </mi> </mrow> </msub> </mrow> </msub> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> m </mi> <mo> &#8805; </mo> <mn> 2 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mi> r </mi> <mo> &#8805; </mo> <mn> 2 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <times /> <apply> <ci> KroneckerDelta </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <ci> m </ci> </apply> </apply> <apply> <ci> KroneckerDelta </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <apply> <plus /> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> n </ci> <apply> <plus /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <apply> <plus /> <ci> m </ci> <ci> r </ci> </apply> </apply> </apply> </apply> <apply> <ci> KroneckerDelta </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <ci> m </ci> </apply> <apply> <ci> Subscript </ci> <ci> n </ci> <apply> <plus /> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> n </ci> <apply> <plus /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <apply> <plus /> <ci> m </ci> <ci> r </ci> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <geq /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> <apply> <geq /> <ci> r </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2007-05-02