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http://functions.wolfram.com/01.02.22.0027.01
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LaplaceTransform[z^t, t, p] == 1/(p - Log[z]) /; Re[Log[z] - p] < 0
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["LaplaceTransform", "[", RowBox[List[SuperscriptBox["z", "t"], ",", "t", ",", "p"]], "]"]], "\[Equal]", FractionBox["1", RowBox[List["p", "-", RowBox[List["Log", "[", "z", "]"]]]]]]], "/;", RowBox[List[RowBox[List["Re", "[", RowBox[List[RowBox[List["Log", "[", "z", "]"]], "-", "p"]], "]"]], "<", "0"]]]]]]
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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> <mrow> <msub> <mi> ℒ </mi> <mi> t </mi> </msub> <mo> [ </mo> <msup> <mi> z </mi> <mi> t </mi> </msup> <mo> ] </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mi> p </mi> <mo> ) </mo> </mrow> </mrow> <mo> ⩵ </mo> <mfrac> <mn> 1 </mn> <mrow> <mi> p </mi> <mo> - </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> Re </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mo> < </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> LaplaceTransform </ci> <apply> <power /> <ci> z </ci> <ci> t </ci> </apply> <ci> t </ci> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <lt /> <apply> <real /> <apply> <plus /> <apply> <ln /> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LaplaceTransform", "[", RowBox[List[SuperscriptBox["z_", "t_"], ",", "t_", ",", "p_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", RowBox[List["p", "-", RowBox[List["Log", "[", "z", "]"]]]]], "/;", RowBox[List[RowBox[List["Re", "[", RowBox[List[RowBox[List["Log", "[", "z", "]"]], "-", "p"]], "]"]], "<", "0"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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