Given a mapping u: [0,+\infty) to X (here X stands for a 
complex Banach space) which admits a holomorphic, bounded 
extension to some sector containing the half axis x<=0, a 
numerical method for inverting the Laplace transform U(z) 
of u is presented. The method uses a classical quadrature 
formula, based on the sinc fonction, and it is shown that 
the classical estimate O(e^{-c sqrt{n}}) improves to 
O(e^{-cn}), where n denotes the number of nodes used in the 
quadrature. One good feature of the method is that the same 
nodes and evaluations of U can be used for intervals [t_0,t_1] 
with large ratios t_1/t_0. The influence of the errors in the 
evalutions of U is also considered.