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 Exp

 http://functions.wolfram.com/01.03.06.0027.01

 Input Form

 HeavisideTheta[x]/E^x \[Proportional] Sum[(-1)^k D[DiracDelta[x], {x, k}], {k, 0, Infinity}]

 Standard Form

 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"]], "}"]]]], "]"]]]]]]]]]]

 MathML Form

 - x θ HeavisideTheta ( x ) k = 0 ( - 1 ) k k δ DiracDelta ( x ) x k Proportional -1 x HeavisideTheta x k 0 -1 k x k DiracDelta x [/itex]

 Rule Form

 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", "]"]]]]]]]]]]]]

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

 2007-05-02