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Exp




Mathematica Notation

Traditional Notation









Elementary Functions > Exp[z] > Integral transforms > Inverse Laplace transforms





http://functions.wolfram.com/01.03.22.0007.01









  


  








Input Form





InverseLaplaceTransform[E^(-t), t, p] == DiracDelta[p - 1] UnitStep[p - 1]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["InverseLaplaceTransform", "[", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "t"]]], ",", "t", ",", "p"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["DiracDelta", "[", RowBox[List["p", "-", "1"]], "]"]], " ", RowBox[List["UnitStep", "[", RowBox[List["p", "-", "1"]], "]"]]]]]]]]








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> <msubsup> <mi> &#8466; </mi> <mi> t </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> [ </mo> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mi> t </mi> </mrow> </msup> <mo> ] </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> p </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mi> &#948; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> p </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> &#952; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> p </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> InverseLaplaceTransform </ci> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> t </ci> </apply> </apply> <ci> t </ci> <ci> p </ci> </apply> <apply> <times /> <apply> <ci> &#948; </ci> <apply> <plus /> <ci> p </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> &#952; </ci> <apply> <plus /> <ci> p </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseLaplaceTransform", "[", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "t_"]]], ",", "t_", ",", "p_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["DiracDelta", "[", RowBox[List["p", "-", "1"]], "]"]], " ", RowBox[List["UnitStep", "[", RowBox[List["p", "-", "1"]], "]"]]]]]]]]


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





2001-10-29