Tables of Integral Transforms

A considerable proportion of the tremendous amount of material collected by the late Professor Harry Bateman concerns definite integrals. The organization and presentation of this material is a very difficult task to which Bateman devoted considerable attention. It is fairly clear that the arrangement used in shorter tables of integrals is not very suitable for a collection about three times the size of Bierens de Haan, and the circumstance that a considerable proportion of these integrals involves higher transcendental functions with their manifold and not always highly standardized notations, does not make this task easier. Eventually, Bateman decided to break up his integral tables into several more or less self-contained parts, classifying integrals according to their fields of application. A collection of integrals occurring in the theory of axially symmetric potentials was prepared, and other similar collections were to follow. Clearly such a plan involves a generous amount of duplication if the resulting tables are to be self-contained, but it also has great advantages from the user's point of view.