Excerpt from The Inverse Laplace Transform of an Exponential Function In electromagnetic problems one often has occasion to study pulse fields, that is, fields created by sources which have a Heaviside unit function behavior or a delta-function behavior in the time variable as well as fields created by the same sources and having a harmonic time behavior. The latter fields also prove to be harmonic in time (apart from a transient) and these time harmonic fields are the Laplace transforms of the corresponding pulse fields. To extend the kwledge of the relationship between time harmonic fields and pulse fields and between the asymptotic series described above and the corresponding series of powers to fields diffracted by smooth bodies, it w appears desirable to utilize some Laplace transforms which have t been established. It is expected that the result will be useful in electromagnetic diffraction problems but the present paper will be devoted to the purely mathematical problem of determining the original function and also the asymptotic behavior of the original function for t near 0. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art techlogy to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.