  A common way to approximate $F(A)b$ -- the action of a matrix function on a
vector -- is to use the Arnoldi approximation. Since a new vector needs to be
generated and stored in every iteration, one is often forced to rely on restart
algorithms which are either not efficient, not stable or only applicable to
restricted classes of functions. We present a new representation of the error
of the Arnoldi iterates if the function $F$ is given as a Laplace transform.
Based on this representation we build an efficient and stable restart
algorithm. In doing so we extend earlier work for the class of Stieltjes
functions which are special Laplace transforms. We report several numerical
experiments including comparisons with the restart method for Stieltjes
functions.
