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Transforms
*INTRO In this chapter, some facilities for various transforms
are described.
*CMD LaplaceTransform  Laplace Transform
*STD
*CALL
LaplaceTransform(t,s,f)
*PARMS
{t}  independent variable that is being transformed
{s}  independent variable that is being transformed into
{f}  function
*DESC
This function attempts to take the function $f(t)$ and find the Laplace transform
of it,$F(s)$, which is defined as $Integrate(t,0,Infinity) Exp(s*t)*f(t)$. This is
also sometimes referred to the "unilateral" Laplace tranform. {LaplaceTransform}
can transform most elementary functions that do not require a convolution integral,
as well as any polynomial times an elementary function. If a transform cannot
be found then {LaplaceTransform} will return unevaluated. This can happen
for function which are not of "exponential order", which means that they grow
faster than exponential functions.
*E.G.
In> LaplaceTransform(t,s,2*t^5+ t^2/2 )
Out> 240/s^6+2/(2*s^3);
In> LaplaceTransform(t,s,t*Sin(2*t)*Exp(3*t) )
Out> (2*(s+3))/(2*(2*(((s+3)/2)^2+1))^2);
In> LaplaceTransform(t,s, BesselJ(3,2*t) )
Out> (Sqrt((s/2)^2+1)s/2)^3/(2*Sqrt((s/2)^2+1));
In> LaplaceTransform(t,s,Exp(t^2)); // not of exponential order
Out> LaplaceTransform(t,s,Exp(t^2));
In> LaplaceTransform(p,q,Ln(p))
Out> (gamma+Ln(q))/q;
