(*:Title: Additional analytical inverse Laplace transforms *)
(*:Mathematica Version: 3.0 *)
(*:Package Version: 1.0 *)
(*:Author: Arnaud Mallet ,University of Mauritius *)
(*:Contact: arnomallet@yahoo.com *)
(*:Copyright: © 2000 by Arnaud Mallet
Permission is hereby granted to make copies of this file for any
purpose other than direct profit, or as part of a commercial product,
provided this copyright notice is left intact.
Sale is prohibited. *)
(*:Note: This package requires the Mathematica packages "Calculus`LaplaceTransform`" & "Calculus`DiracDelta`" *)
(*:Overview: This package provides additional exact inverse Laplace transforms definitions
such as: BesselK[n,a s], Sinh[a/s], Sinh[a/s]/Sqrt[s], s Log[a s]/(s^2+1), etc.
Mathematica version 3.0 cannot invert such types of functions that arise in many
applied Maths problems. *)
(*:Limitations: The inverse Laplace transform of BesselK[n,a s] should be used with positive a only. *)
(*:Precaution: Ensure that the Packages "Calculus`LaplaceTransform`" & "Calculus`DiracDelta`" are
available, else the functions requiring Convolution will not be evaluated *)
(*:Examples: See the Mathematica notebook example.nb that comes with the package *)
BeginPackage[ "MoreInvLaplace`" ,"Calculus`DiracDelta`","Calculus`LaplaceTransform`"]
Clear[RectangularWave];
RectangularWave::usage="
RectangularWave[a,t] , is a Rectangular wave with amplitude 1 and period 2a (a>0).\n
Let F[t]=RectangularWave[a,t], then F[t]=1 for 0