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variants of this functions
DiracDelta




Mathematica Notation

Traditional Notation









Generalized Functions > DiracDelta[x] > Limit representations





http://functions.wolfram.com/14.03.09.0007.01









  


  








Input Form





DiracDelta[x] == Limit[Log[Abs[Coth[a x]]], a -> Infinity]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["DiracDelta", "[", "x", "]"]], "\[Equal]", RowBox[List["Limit", "[", RowBox[List[RowBox[List["Log", "[", RowBox[List["Abs", "[", RowBox[List["Coth", "[", RowBox[List["a", " ", "x"]], "]"]], "]"]], "]"]], ",", RowBox[List["a", "\[Rule]", "\[Infinity]"]]]], "]"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> DiracDelta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <munder> <mi> lim </mi> <mrow> <mi> a </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mi> &#8734; </mi> </mrow> </munder> <mo> &#8290; </mo> <mtext> &#8201; </mtext> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mrow> <mi> coth </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> x </mi> </mrow> <mo> ) </mo> </mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> DiracDelta </ci> <ci> x </ci> </apply> <apply> <limit /> <bvar> <ci> a </ci> </bvar> <condition> <apply> <tendsto /> <ci> a </ci> <infinity /> </apply> </condition> <apply> <ln /> <apply> <abs /> <apply> <coth /> <apply> <times /> <ci> a </ci> <ci> x </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DiracDelta", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Limit", "[", RowBox[List[RowBox[List["Log", "[", RowBox[List["Abs", "[", RowBox[List["Coth", "[", RowBox[List["a", " ", "x"]], "]"]], "]"]], "]"]], ",", RowBox[List["a", "\[Rule]", "\[Infinity]"]]]], "]"]]]]]]


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





2001-10-29