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variants of this functions
DiracDelta




Mathematica Notation

Traditional Notation









Generalized Functions > DiracDelta[x] > Integral transforms > Fourier exp transforms





http://functions.wolfram.com/14.03.22.0008.01









  


  








Input Form





FourierTransform[DiracComb[t], t, x] == (1/Sqrt[2 Pi]) DiracComb[x/(2 Pi)]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["FourierTransform", "[", RowBox[List[RowBox[List["DiracComb", "[", "t", "]"]], ",", "t", ",", "x"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]]], RowBox[List["DiracComb", "[", FractionBox["x", RowBox[List["2", "\[Pi]"]]], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msub> <mi> &#8497; </mi> <mi> t </mi> </msub> <mo> [ </mo> <mrow> <mi> DiracComb </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> t </mi> <mo> ) </mo> </mrow> <mo> ] </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#63449; </mo> <mrow> <mfrac> <mn> 1 </mn> <msqrt> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </msqrt> </mfrac> <mo> &#8290; </mo> <mrow> <mi> DiracComb </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> x </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> FourierTransform </ci> <apply> <ci> DiracComb </ci> <ci> t </ci> </apply> <ci> t </ci> <ci> x </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> DiracComb </ci> <apply> <times /> <ci> x </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["FourierTransform", "[", RowBox[List[RowBox[List["DiracComb", "[", "t_", "]"]], ",", "t_", ",", "x_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["DiracComb", "[", FractionBox["x", RowBox[List["2", " ", "\[Pi]"]]], "]"]], SqrtBox[RowBox[List["2", " ", "\[Pi]"]]]]]]]]


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





2007-05-02