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variants of this functions
HeavisideTheta




Mathematica Notation

Traditional Notation









Generalized Functions > HeavisideTheta[x1,x2,...] > Differentiation > Low-order differentiation





http://functions.wolfram.com/14.06.20.0001.01









  


  








Input Form





D[HeavisideTheta[Subscript[x, 1], Subscript[x, 2], \[Ellipsis]], Subscript[x, 1]] == DiracDelta[Subscript[x, 1]] HeavisideTheta[Subscript[x, 2], \[Ellipsis]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", SubscriptBox["x", "1"]], RowBox[List["HeavisideTheta", "[", RowBox[List[SubscriptBox["x", "1"], ",", SubscriptBox["x", "2"], ",", "\[Ellipsis]"]], "]"]]]], "\[Equal]", RowBox[List[RowBox[List["DiracDelta", "[", SubscriptBox["x", "1"], "]"]], " ", RowBox[List["HeavisideTheta", "[", RowBox[List[SubscriptBox["x", "2"], ",", "\[Ellipsis]"]], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <semantics> <mi> &#952; </mi> <annotation-xml encoding='MathML-Content'> <ci> HeavisideTheta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> x </mi> <mn> 2 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <msub> <mi> x </mi> <mn> 1 </mn> </msub> </mrow> </mfrac> <mo> &#63449; </mo> <mrow> <mrow> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> DiracDelta </ci> </annotation-xml> </semantics> <mo> ( </mo> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <semantics> <mi> &#952; </mi> <annotation-xml encoding='MathML-Content'> <ci> HeavisideTheta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <msub> <mi> x </mi> <mn> 2 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> D </ci> <apply> <ci> HeavisideTheta </ci> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <ci> &#8230; </ci> </apply> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <apply> <ci> DiracDelta </ci> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> HeavisideTheta </ci> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <ci> &#8230; </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[SubscriptBox["x_", "1"]]]], RowBox[List["HeavisideTheta", "[", RowBox[List[SubscriptBox["x_", "1"], ",", SubscriptBox["x_", "2"], ",", "\[Ellipsis]_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["DiracDelta", "[", SubscriptBox["xx", "1"], "]"]], " ", RowBox[List["HeavisideTheta", "[", RowBox[List[SubscriptBox["xx", "2"], ",", "\[Ellipsis]"]], "]"]]]]]]]]


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





2007-05-02