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variants of this functions
DiracDelta




Mathematica Notation

Traditional Notation









Generalized Functions > DiracDelta[x] > Transformations > Transformations and argument simplifications





http://functions.wolfram.com/14.03.16.0001.01









  


  








Input Form





DiracDelta[a x] == DiracDelta[x]/Abs[a] /; Element[a, Reals]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["DiracDelta", "[", RowBox[List["a", " ", "x"]], "]"]], "\[Equal]", FractionBox[RowBox[List["DiracDelta", "[", "x", "]"]], RowBox[List["Abs", "[", "a", "]"]]]]], "/;", RowBox[List["a", "\[Element]", "Reals"]]]]]]








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> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> DiracDelta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> x </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> DiracDelta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mi> a </mi> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> </mfrac> </mrow> <mo> /; </mo> <mrow> <mi> a </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> DiracDelta </ci> <apply> <times /> <ci> a </ci> <ci> x </ci> </apply> </apply> <apply> <times /> <apply> <ci> DiracDelta </ci> <ci> x </ci> </apply> <apply> <power /> <apply> <abs /> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <in /> <ci> a </ci> <reals /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DiracDelta", "[", RowBox[List["a_", " ", "x_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["DiracDelta", "[", "x", "]"]], RowBox[List["Abs", "[", "a", "]"]]], "/;", RowBox[List["a", "\[Element]", "Reals"]]]]]]]]


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





2001-10-29