Laplace vs. Inverse Laplace Transforms in Mathematica v4
- To: mathgroup at smc.vnet.net
- Subject: [mg19985] Laplace vs. Inverse Laplace Transforms in Mathematica v4
- From: "Will Cooper" <wcooper1 at san.rr.com>
- Date: Thu, 23 Sep 1999 23:26:29 -0400
- Organization: Time Warner Cable of San Diego, CA
- Sender: owner-wri-mathgroup at wolfram.com
Hello, I can perform Laplace Transforms in Mathematica version 4 with no problems. However, I'm having problems getting Mathematica to do certain inverse Laplace Transforms. I attach a notebook showing both a successful and an unsucessful Inverse Laplace Transform calculation. Please can you help. Thanks, Will Cooper. Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. 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\ \ \[IndentingNewLine]\[IndentingNewLine]HOW\ CAN\ I\ GET\ THE\ INVERSE\ LAPLACE\ \ TRANSFORM\ OF\ THIS\ FUNCTION?\ \[IndentingNewLine]\[IndentingNewLine]ANY\ \ HELP\ WOULD\ BE\ GREATLY\ APPRECIATED . \ \[IndentingNewLine]\[IndentingNewLine]openloopnakrv[a_, m_, \[CapitalOmega]_, z_] := \(2\ a\^\(a + 1\/2\ \((\(-a\) + m)\)\)\ z\^\(\(-1\) + \ m\)\ \((m\/\[CapitalOmega])\)\^m\ \((\[CapitalOmega]\/\(m\ z\))\)\^\(1\/2\ \ \((\(-a\) + m)\)\)\ BesselK[\(-a\) + m, 2\ \ at a\ \ at \(\(m\ z\)\/\[CapitalOmega]\ \)]\)\/\(Gamma[a]\ Gamma[m]\)\[IndentingNewLine]\), "\[IndentingNewLine]", \(LaplaceTransform[openloopnakrv[a, m, \[CapitalOmega], z], z, \[Omega]]\)}], "Input"], Cell[BoxData[ \(\(1\/\(Gamma[a]\ Gamma[ m]\)\) \((a\^\(a + 1\/2\ \((\(-a\) + m)\)\)\ \[Omega]\^\(\(-a\) \ - m\)\ \((m\/\[CapitalOmega])\)\^m\ \((\(a\ m\)\/\[CapitalOmega])\)\^\(1\/2\ \ \((\(-a\) - m)\)\)\ \((\[CapitalOmega]\/m)\)\^\(1\/2\ \((\(-a\) + m)\)\)\ \((\ \[Omega]\^m\ \((\(a\ m\)\/\[CapitalOmega])\)\^a\ Gamma[ a]\ Gamma[\(-a\) + m]\ Hypergeometric1F1[a, 1 + a - 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a + m, \(a\ m\)\/\(\[Omega]\ \[CapitalOmega]\)])\), \ \[Omega], z])\)\)], "Output"] }, Open ]], Cell[BoxData[ \(FAILS\ TO\ \(CALCULATE!\)\)], "Input"] }, FrontEndVersion->"4.0 for Microsoft Windows", ScreenRectangle->{{0, 1024}, {0, 695}}, WindowSize->{911, 668}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, PrintingCopies->1, PrintingPageRange->{Automatic, Automatic}, PrintingOptions->{"PrintingMargins"->{{18, 18}, {36, 72}}, "PrintCellBrackets"->False, "PrintRegistrationMarks"->True, "PrintMultipleHorizontalPages"->False} ] (*********************************************************************** Cached data follows. 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