Hi, I need to obtain explicit formulae for the inverse Laplace transform: F[k_] = InverseLaplaceTransform[((s/(s + 1))^(k/2))/s, s, t] for k=1,2,... MATHEMATICA returns an expression involving some Laguerre polynomial, but I have reasons to believe that the result can be expressed by some combinations of exponentials and exponentially scaled Bessel functions BesselI[0,t/2] and BesselI[1,t/2]. Indeed, after many unsuccessfull attempts, I find that Table[FunctionExpand[F[i]], {i, 1, 25}] produces a desired result. Unfortunately it fails in the case of i=15, 17, 19, etc. Is there any way to force FunctionExpand[] to provide the relevant expression also in these cases? I also note that (for unclear reasons) InverseLaplaceTransform[] fails to provide the inverse in the case when for example, I enter Sqrt[s/(s+1)]/s, although this is a special case of the above general formula. Lesław
