Hi, I am trying to obtain the inverse Laplace transform:
InverseLaplaceTransform[(1 + (-1 + g)*Sqrt[s]*((-3 + g)*Sqrt[s] + 2*(-1 + g)*s^(3/2) + 2*Sqrt[1 + s] -
2*(-1 + g)*s*Sqrt[1 + s]))/s,s,t]
where g>0. Mathematica cannot determine it. I have reasons to suspect, however, that the inverse exists and involves exponentially scaled Bessel functions: Exp[-t/2]*BesselI[0,t/2] and Exp[-t/2]*BesselI[1,t/2] . Is there any way to obtain such a result, or to prove without any doubt (by using Mathematica) that the inverse does not exist?
Leslaw