x^n Derivative[m][DiracDelta][x] == 0 /; Element[m, Integers] && Element[n, Integers] && Inequality[0, LessEqual, m, Less, 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> <msup> <mi> x </mi> <mi> n </mi> </msup> <mo> &#8290; </mo> <mrow> <msup> <mi> &#948; </mi> <semantics> <mrow> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, &quot;m&quot;, &quot;)&quot;]], Derivative] </annotation> </semantics> </msup> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> m </mi> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mn> 0 </mn> <mo> &#8804; </mo> <mi> m </mi> <mo> &lt; </mo> <mi> n </mi> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <times /> <apply> <power /> <ci> x </ci> <ci> n </ci> </apply> <apply> <partialdiff /> <bvar> <ci> x </ci> <degree> <ci> m </ci> </degree> </bvar> <apply> <ci> &#948; </ci> <ci> x </ci> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <and /> <apply> <in /> <ci> m </ci> <integers /> </apply> <apply> <in /> <ci> n </ci> <integers /> </apply> <apply> <ci> Inequality </ci> <cn type='integer'> 0 </cn> <leq /> <ci> m </ci> <lt /> <ci> n </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2001-10-29