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 Exp

 http://functions.wolfram.com/01.03.06.0029.01

 Input Form

 E^(-Abs[x]) \[Proportional] 2 Sum[k! D[DiracDelta[x], {x, 2 k}], {k, 0, Infinity}]

 Standard Form

 Cell[BoxData[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", RowBox[List["Abs", "[", "x", "]"]]]]], "\[Proportional]", RowBox[List["2", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[RowBox[List["k", "!"]], RowBox[List["D", "[", RowBox[List[RowBox[List["DiracDelta", "[", "x", "]"]], ",", RowBox[List["{", RowBox[List["x", ",", RowBox[List["2", "k"]]]], "}"]]]], "]"]]]]]]]]]]]]

 MathML Form

 - "\[LeftBracketingBar]" x "\[RightBracketingBar]" 2 k = 0 k ! 2 k δ DiracDelta ( x ) x 2 k Proportional -1 x 2 k 0 k x 2 k DiracDelta x [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["\[ExponentialE]", RowBox[List["-", RowBox[List["Abs", "[", "x_", "]"]]]]], "]"]], "\[RuleDelayed]", RowBox[List["2", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[RowBox[List["k", "!"]], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["x", ",", RowBox[List["2", " ", "k"]]]], "}"]]]]], RowBox[List["DiracDelta", "[", "x", "]"]]]]]]]]]]]]]]

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

 2007-05-02