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Published 1954 | Published
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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.

Additional Information

Based, in part, on notes left by Harry Bateman Late Professor of Mathematics, Theoretical Physics, and Aeronautics at the California Institute of Technology and compiled by the Staff of the Bateman Manuscript Project. Prepared at the California Institute of Technology under Contract No. N6onr-244 Task Order XIV with the Office of Naval Research. Project Designation Number: NR 043-045. This work is dedicated to the memory of HARRY BATEMAN as a tribute to the imagination which led him to undertake a project of this magnitude, and the scholarly dedication which inspired him to carry it so far toward completion. It is a pleasant duty to express the thanks of the California Institute of Technology to the family of the late Professor Bateman for the gift of his notes and library, and to the Office of Naval Research for the generous support they have given to this work, and for the understanding they have constantly shown for the difficulties encountered. The Institute also wishes to record its appreciation and thanks to the late Professor A.D. Michal for his preliminary survey of Bateman's notes; to the University of Edinburgh for granting leave of absence to the undersigned; to the Rockefeller Foundation for making a grant towards traveling expenses; and to the McGraw-Hill Company for technical advice and publication. The Editor wishes to acknowledge his indebtedness to practically all the published integral tables which have been consulted in the course of the work on the present tables; and he wishes to express his thanks to his colleagues, especially the Research Assistants who played such an important part in the compilation. Corrections of errors, additions, and suggestion for improvement will be gratefully received by the Editor.

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August 19, 2023
October 25, 2023