  We consider the problem of finding a function defined on $(0,\infty)$ from a
countable set of values of its Laplace transform. The problem is severely
ill-posed. We shall use the expansion of the function in a series of Laguerre
polynomials to convert the problem in an analytic interpolation problem. Then,
using the coefficients of Lagrange polynomials we shall construct a stable
approximation solution.
