InverseLaplaceTransform[Sqrt[t], t, p] == -(1/(2 p^(3/2) Sqrt[Pi]))

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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> &#8466; </mi> <mi> t </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> [ </mo> <msqrt> <mi> t </mi> </msqrt> <mo> ] </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> p </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> p </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> InverseLaplaceTransform </ci> <apply> <power /> <ci> t </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> t </ci> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> p </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseLaplaceTransform", "[", RowBox[List[SqrtBox["t_"], ",", "t_", ",", "p_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox["1", RowBox[List["2", " ", SuperscriptBox["p", RowBox[List["3", "/", "2"]]], " ", SqrtBox["\[Pi]"]]]]]]]]]]

2001-10-29