I need to find an inverse Laplace transform of the expression:
where "s" is the Laplace variable, "a" is a real positive constant, and "b" is a real constant that can be either positive or negative. I have tried the InverseLaplaceTransform function, but it returns the original expression. My question is: does this mean that the inverse transform does not exist, or only Mathematica cannot find it? Also, if anybody knows where I could possibly find the inverse in any book, or how I might obtain the inverse otherwise, I would appreciate an information. Abramowitz and Stegun book does not have it.