html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 DiracDelta

 http://functions.wolfram.com/14.03.07.0006.01

 Input Form

 D[DiracDelta[x], x] == (1/(2 Pi I)) Integrate[t Exp[(-I) x t], {t, -Infinity, Infinity}]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["D", "[", RowBox[List[RowBox[List["DiracDelta", "[", "x", "]"]], ",", "x"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2", "\[Pi]", " ", "\[ImaginaryI]"]]], RowBox[List[SubsuperscriptBox["\[Integral]", RowBox[List["-", "\[Infinity]"]], "\[Infinity]"], RowBox[List["t", " ", RowBox[List["Exp", "[", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "x", " ", "t"]], "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]]]]

 MathML Form

 δ DiracDelta ( x ) x 1 2 π - t - x t t x DiracDelta x 1 2 -1 t -1 t -1 x t [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["x_"]]], RowBox[List["DiracDelta", "[", "x_", "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SubsuperscriptBox["\[Integral]", RowBox[List["-", "\[Infinity]"]], "\[Infinity]"], RowBox[List[RowBox[List["t", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "x", " ", "t"]]]]], RowBox[List["\[DifferentialD]", "t"]]]]]], RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]"]]]]]]]

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

 2007-05-02