An Inversion Technique for the Laplace Transform with Application to Approximation

An Inversion Technique for the Laplace Transform with Application to Approximation By D. L. JAGERMAN (Manuscript received July 26, 1977) Properties of a sequence of positive operators defined by the Widder Laplace inversion formula are studied in order to obtain practical methods for the inversion of the Laplace transform, practical error formulae, and useful approximations to given functions. The approximation procedure retains essential structural characteristics of the original function, e.g., nonnegativity, monotonicity, and convexity. Thus a distribution function is approximated by distribution functions. Enhancement techniques are provided for the improvement of accuracy for a given order of approximation. The methods are illustrated by applications to renewal theory and to the covariance and recovery functions of telephone traffic theory.