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http://functions.wolfram.com/04.18.07.0001.01
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DiscreteDelta[n] == (1/(2 Pi)) Integrate[E^(I t n), {t, 0, 2 Pi}]
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Cell[BoxData[RowBox[List[RowBox[List["DiscreteDelta", "[", "n", "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2", "\[Pi]"]]], " ", RowBox[List[SubsuperscriptBox["\[Integral]", "0", RowBox[List["2", "\[Pi]"]]], " ", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "t", " ", "n"]]], " ", RowBox[List["\[DifferentialD]", "t"]]]]]]]]]]]]
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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> <semantics> <mi> δ </mi> <annotation-xml encoding='MathML-Content'> <ci> DiscreteDelta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <msubsup> <mo> ∫ </mo> <mn> 0 </mn> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </msubsup> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> t </mi> <mo> ⁢ </mo> <mi> n </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> t </mi> </mrow> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> DiscreteDelta </ci> <ci> n </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <int /> <bvar> <ci> t </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </uplimit> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <ci> t </ci> <ci> n </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DiscreteDelta", "[", "n_", "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SubsuperscriptBox["\[Integral]", "0", RowBox[List["2", " ", "\[Pi]"]]], RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "t", " ", "n"]]], RowBox[List["\[DifferentialD]", "t"]]]]]], RowBox[List["2", " ", "\[Pi]"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
