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http://functions.wolfram.com/02.01.22.0006.01
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InverseLaplaceTransform[I, t, z] == I DiracDelta[z]
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Cell[BoxData[RowBox[List[RowBox[List["InverseLaplaceTransform", "[", RowBox[List["\[ImaginaryI]", ",", "t", ",", "z"]], "]"]], "\[Equal]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["DiracDelta", "[", "z", "]"]]]]]]]]
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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> <mrow> <msubsup> <mi> ℒ </mi> <mi> t </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> [ </mo> <mi> ⅈ </mi> <mo> ] </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <semantics> <mi> δ </mi> <annotation-xml encoding='MathML-Content'> <ci> DiracDelta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> InverseLaplaceTransform </ci> <imaginaryi /> <ci> t </ci> <ci> z </ci> </apply> <apply> <times /> <imaginaryi /> <apply> <ci> DiracDelta </ci> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseLaplaceTransform", "[", RowBox[List["\[ImaginaryI]", ",", "t_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["DiracDelta", "[", "z", "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
