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http://functions.wolfram.com/14.04.21.0001.01
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Integrate[DiracDelta[Subscript[t, 1], Subscript[t, 2], …, Subscript[t, n]],
{Subscript[t, 1], -Infinity, Infinity}, {Subscript[t, 2], -Infinity, Infinity},
…, {Subscript[t, n], -Infinity, Infinity}] == 1
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Cell[BoxData[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", InterpretationBox[RowBox[List["-", "\[Infinity]"]], DirectedInfinity[-1]], InterpretationBox["\[Infinity]", DirectedInfinity[1]]], RowBox[List[SubsuperscriptBox["\[Integral]", InterpretationBox[RowBox[List["-", "\[Infinity]"]], DirectedInfinity[-1]], InterpretationBox["\[Infinity]", DirectedInfinity[1]]], RowBox[List["\[Ellipsis]", RowBox[List[SubsuperscriptBox["\[Integral]", InterpretationBox[RowBox[List["-", "\[Infinity]"]], DirectedInfinity[-1]], InterpretationBox["\[Infinity]", DirectedInfinity[1]]], RowBox[List[RowBox[List["DiracDelta", "[", 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]", "1"]]]]
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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> <msubsup> <mo> ∫ </mo> <semantics> <mrow> <mo> - </mo> <mi> ∞ </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <times /> <cn type='integer'> -1 </cn> <infinity /> </apply> </annotation-xml> </semantics> <semantics> <mi> ∞ </mi> <annotation-xml encoding='MathML-Content'> <infinity /> </annotation-xml> </semantics> </msubsup> <mrow> <msubsup> <mo> ∫ </mo> <semantics> <mrow> <mo> - </mo> <mi> ∞ </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <times /> <cn type='integer'> -1 </cn> <infinity /> </apply> </annotation-xml> </semantics> <semantics> <mi> ∞ </mi> <annotation-xml encoding='MathML-Content'> <infinity /> </annotation-xml> </semantics> </msubsup> <mrow> <mo> … </mo> <mo> ⁢ </mo> <mrow> <msubsup> <mo> ∫ </mo> <semantics> <mrow> <mo> - </mo> <mi> ∞ </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <times /> <cn type='integer'> -1 </cn> <infinity /> </apply> </annotation-xml> </semantics> <semantics> <mi> ∞ </mi> <annotation-xml encoding='MathML-Content'> <infinity /> </annotation-xml> </semantics> </msubsup> <mrow> <mrow> <semantics> <mi> δ </mi> <annotation-xml encoding='MathML-Content'> <ci> DiracDelta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <msub> <mi> t </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> t </mi> <mn> 2 </mn> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <msub> <mi> t </mi> <mi> n </mi> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <msub> <mi> t </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <msub> <mi> t </mi> <mn> 2 </mn> </msub> </mrow> <mo> ⁢ </mo> <mo> … </mo> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <msub> <mi> t </mi> <mi> n </mi> </msub> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mn> 1 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <msubsup> <mo> ∫ </mo> <semantics> <mrow> <mo> - </mo> <mi> ∞ </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <times /> <cn type='integer'> -1 </cn> <infinity /> </apply> </annotation-xml> </semantics> <semantics> <mi> ∞ </mi> <annotation-xml encoding='MathML-Content'> <infinity /> </annotation-xml> </semantics> </msubsup> <mrow> <msubsup> <mo> ∫ </mo> <semantics> <mrow> <mo> - </mo> <mi> ∞ </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <times /> <cn type='integer'> -1 </cn> <infinity /> </apply> </annotation-xml> </semantics> <semantics> <mi> ∞ </mi> <annotation-xml encoding='MathML-Content'> <infinity /> </annotation-xml> </semantics> </msubsup> <mrow> <mo> … </mo> <mo> ⁢ </mo> <mrow> <msubsup> <mo> ∫ </mo> <semantics> <mrow> <mo> - </mo> <mi> ∞ </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <times /> <cn type='integer'> -1 </cn> <infinity /> </apply> </annotation-xml> </semantics> <semantics> <mi> ∞ </mi> <annotation-xml encoding='MathML-Content'> <infinity /> </annotation-xml> </semantics> </msubsup> <mrow> <mrow> <semantics> <mi> δ </mi> <annotation-xml encoding='MathML-Content'> <ci> DiracDelta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <msub> <mi> t </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> t </mi> <mn> 2 </mn> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <msub> <mi> t </mi> <mi> n </mi> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <msub> <mi> t </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <msub> <mi> t </mi> <mn> 2 </mn> </msub> </mrow> <mo> ⁢ </mo> <mo> … </mo> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <msub> <mi> t </mi> <mi> n </mi> </msub> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mn> 1 </mn> </mrow> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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© 1998-2013 Wolfram Research, Inc.
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){kind=small}
