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variants of this functions
DiracDelta




Mathematica Notation

Traditional Notation









Generalized Functions > DiracDelta[x] > Identities > Functional identities





http://functions.wolfram.com/14.03.17.0002.01









  


  








Input Form





DiracDelta[Subscript[x, 1] - Subscript[x, 0]] DiracDelta[Subscript[x, 2] - Subscript[x, 0]] == DiracDelta[Subscript[x, 2] - Subscript[x, 1]] DiracDelta[Subscript[x, 1] - Subscript[x, 0]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["DiracDelta", "[", RowBox[List[SubscriptBox["x", "1"], "-", SubscriptBox["x", "0"]]], "]"]], RowBox[List["DiracDelta", "[", RowBox[List[SubscriptBox["x", "2"], "-", SubscriptBox["x", "0"]]], "]"]]]], "\[Equal]", RowBox[List[RowBox[List["DiracDelta", "[", RowBox[List[SubscriptBox["x", "2"], "-", SubscriptBox["x", "1"]]], "]"]], RowBox[List["DiracDelta", "[", RowBox[List[SubscriptBox["x", "1"], "-", SubscriptBox["x", "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> <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> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> DiracDelta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <msub> <mi> x </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> x </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <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> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> DiracDelta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <msub> <mi> x </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> x </mi> <mn> 1 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <ci> DiracDelta </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <apply> <ci> DiracDelta </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ci> DiracDelta </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <apply> <ci> DiracDelta </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["DiracDelta", "[", RowBox[List[SubscriptBox["x_", "1"], "-", SubscriptBox["x_", "0"]]], "]"]], " ", RowBox[List["DiracDelta", "[", RowBox[List[SubscriptBox["x_", "2"], "-", SubscriptBox["x_", "0"]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["DiracDelta", "[", RowBox[List[SubscriptBox["xx", "2"], "-", SubscriptBox["xx", "1"]]], "]"]], " ", RowBox[List["DiracDelta", "[", RowBox[List[SubscriptBox["xx", "1"], "-", SubscriptBox["xx", "0"]]], "]"]]]]]]]]


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





2007-05-02