The Approximation Sequence of the Laplace Transform

The approximation sequence is defined and studied. The sequence is the basis of the method of accurate Laplace transform inversion commonly used. It is shown how, by means of the approximation sequence, simple analytic approximations may be constructed and also practical numerical solution of the important M/G/1/L queue both in equilibrium and in transient modes (L refers to the maximum work capacity of the queue).