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variants of this functions
DiracDelta






Mathematica Notation

Traditional Notation









Generalized Functions > DiracDelta[x1,x2,...] > Integration > Definite integration > Multiple integration





http://functions.wolfram.com/14.04.21.0002.01









  


  










Input Form





Integrate[DiracDelta[Subscript[t, 1] - Subscript[a, 1], Subscript[t, 2] - Subscript[a, 2], …, Subscript[t, n] - Subscript[a, n]]* f[Subscript[t, 1], Subscript[t, 2], …, Subscript[t, n]], {Subscript[t, 1], -Subscript[d, 1], Subscript[d, 1]}, {Subscript[t, 2], -Subscript[d, 2], Subscript[d, 2]}, …, {Subscript[t, n], -Subscript[d, n], Subscript[d, n]}] == 1/; Inequality[-Infinity, LessEqual, -Subscript[d, k], Less, Subscript[a, k], Less, Subscript[d, k], LessEqual, Infinity] && 1 <= k <= n










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", InterpretationBox[RowBox[List["-", SubscriptBox["d", "1"]]], DirectedInfinity[-1]], InterpretationBox[SubscriptBox["d", "1"], DirectedInfinity[1]]], RowBox[List[SubsuperscriptBox["\[Integral]", InterpretationBox[RowBox[List["-", SubscriptBox["d", "2"]]], DirectedInfinity[-1]], SubscriptBox["d", "2"]], RowBox[List["\[Ellipsis]", RowBox[List[SubsuperscriptBox["\[Integral]", InterpretationBox[RowBox[List["-", SubscriptBox["d", "n"]]], DirectedInfinity[-1]], InterpretationBox[SubscriptBox["d", "n"], DirectedInfinity[1]]], RowBox[List[RowBox[List["DiracDelta", "[", RowBox[List[RowBox[List[SubscriptBox["t", "1"], "-", SubscriptBox["a", "1"]]], ",", RowBox[List[SubscriptBox["t", "2"], "-", SubscriptBox["a", "2"]]], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["t", "n"], "-", SubscriptBox["a", "n"]]]]], "]"]], RowBox[List["f", "[", RowBox[List[SubscriptBox["t", "1"], ",", SubscriptBox["t", "2"], ",", "\[Ellipsis]", ",", SubscriptBox["t", "n"]]], "]"]], RowBox[List["\[DifferentialD]", SubscriptBox["t", "1"]]], RowBox[List["\[DifferentialD]", SubscriptBox["t", "2"]]], " ", "\[Ellipsis]", RowBox[List["\[DifferentialD]", SubscriptBox["t", "n"]]]]]]]]]]]]], "\[Equal]", RowBox[List["f", "[", RowBox[List[SubscriptBox["a", "1"], ",", SubscriptBox["a", "2"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "n"]]], "]"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["-", "\[Infinity]"]], "\[LessEqual]", RowBox[List["-", SubscriptBox["d", "k"]]], "<", SubscriptBox["a", "k"], "<", SubscriptBox["d", "k"], "\[LessEqual]", "\[Infinity]"]], "\[And]", RowBox[List["1", "\[LessEqual]", "k", "\[LessEqual]", "n"]]]]]]]]










MathML Form







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





2001-10-29





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