Application of best rational function approximation for Laplace transform inversion

The application of a method of least squares Laplace transform inversion due to the author is discussed, and examples are given, which also serve to give us best trigonometric and exponential function approximations to some known functions. In particular the unit step function H(t-1) is considered, and the “best” approximations obtained for it would seem to have application in electrical network theory, including the design of delay lines.