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variants of this functions
DiracDelta




Mathematica Notation

Traditional Notation









Generalized Functions > DiracDelta[x] > Differentiation > Symbolic differentiation





http://functions.wolfram.com/14.03.20.0001.01









  


  








Input Form





Derivative[n][DiracDelta][-x] == (-1)^n Derivative[n][DiracDelta][x] /; Element[n, Integers] && n >= 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["DiracDelta", TagBox[RowBox[List["(", "n", ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["-", "x"]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], RowBox[List[SuperscriptBox["DiracDelta", TagBox[RowBox[List["(", "n", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "x", "]"]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "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> <msup> <mi> &#948; </mi> <semantics> <mrow> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, &quot;n&quot;, &quot;)&quot;]], Derivative] </annotation> </semantics> </msup> <mo> ( </mo> <mrow> <mo> - </mo> <mi> x </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mo> &#8290; </mo> <mrow> <msup> <mi> &#948; </mi> <semantics> <mrow> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, &quot;n&quot;, &quot;)&quot;]], Derivative] </annotation> </semantics> </msup> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> D </ci> <apply> <ci> &#948; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> x </ci> </apply> </apply> <list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> x </ci> </apply> <ci> n </ci> </list> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <partialdiff /> <bvar> <ci> x </ci> <degree> <ci> n </ci> </degree> </bvar> <apply> <ci> &#948; </ci> <ci> x </ci> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <ci> &#8469; </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox["DiracDelta", TagBox[RowBox[List["(", "n", ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["-", "x_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List[SuperscriptBox["DiracDelta", TagBox[RowBox[List["(", "n", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "x", "]"]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]


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





2001-10-29