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 | | http://functions.wolfram.com/01.03.06.0027.01 | 
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 | | HeavisideTheta[x]/E^x \[Proportional] Sum[(-1)^k D[DiracDelta[x], {x, k}], 
  {k, 0, Infinity}] | 
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 | | Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "x"]]], RowBox[List["HeavisideTheta", "[", "x", "]"]]]], "\[Proportional]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], RowBox[List["D", "[", RowBox[List[RowBox[List["DiracDelta", "[", "x", "]"]], ",", RowBox[List["{", RowBox[List["x", ",", "k"]], "}"]]]], "]"]]]]]]]]]] | 
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   <math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'>  <semantics>  <mrow>  <mrow>  <msup>  <mi> ⅇ </mi>  <mrow>  <mo> - </mo>  <mi> x </mi>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <semantics>  <mi> θ </mi>  <annotation-xml encoding='MathML-Content'>  <ci> HeavisideTheta </ci>  </annotation-xml>  </semantics>  <mo> ( </mo>  <mi> x </mi>  <mo> ) </mo>  </mrow>  </mrow>  <mo> ∝ </mo>  <mrow>  <munderover>  <mo> ∑ </mo>  <mrow>  <mi> k </mi>  <mo> = </mo>  <mn> 0 </mn>  </mrow>  <mi> ∞ </mi>  </munderover>  <mrow>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mi> k </mi>  </msup>  <mo> ⁢ </mo>  <mfrac>  <mrow>  <msup>  <mo> ∂ </mo>  <mi> k </mi>  </msup>  <mrow>  <semantics>  <mi> δ </mi>  <annotation-xml encoding='MathML-Content'>  <ci> DiracDelta </ci>  </annotation-xml>  </semantics>  <mo> ( </mo>  <mi> x </mi>  <mo> ) </mo>  </mrow>  </mrow>  <mrow>  <mo> ∂ </mo>  <msup>  <mi> x </mi>  <mi> k </mi>  </msup>  </mrow>  </mfrac>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <ci> Proportional </ci>  <apply>  <times />  <apply>  <power />  <exponentiale />  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> x </ci>  </apply>  </apply>  <apply>  <ci> HeavisideTheta </ci>  <ci> x </ci>  </apply>  </apply>  <apply>  <sum />  <bvar>  <ci> k </ci>  </bvar>  <lowlimit>  <cn type='integer'> 0 </cn>  </lowlimit>  <uplimit>  <infinity />  </uplimit>  <apply>  <times />  <apply>  <power />  <cn type='integer'> -1 </cn>  <ci> k </ci>  </apply>  <apply>  <partialdiff />  <bvar>  <ci> x </ci>  <degree>  <ci> k </ci>  </degree>  </bvar>  <apply>  <ci> DiracDelta </ci>  <ci> x </ci>  </apply>  </apply>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "x_"]]], " ", RowBox[List["HeavisideTheta", "[", "x_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["x", ",", "k"]], "}"]]]]], RowBox[List["DiracDelta", "[", "x", "]"]]]]]]]]]]]] | 
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 | | Date Added to functions.wolfram.com (modification date) | 
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