CaltechAUTHORS: Book
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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenMon, 09 Sep 2024 18:50:31 -0700Higher Transcendental Functions [Volumes I-III]
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Year: 1953
The work of which this book is the first volume might be described as an up-to-date version of Part II. The Transcendental Functions of Whittaker and Watson's celebrated "Modern Analysis". Bateman (who was a pupil of E. T. Whittaker) planned his "Guide to the Functions" on a gigantic scale. In addition to a detailed account of the properties of the most important functions, the work was to include the historic origin and definition of, the basic formulas relating to, and a bibliography for all special functions ever invented or investigated. These functions were to be catalogued and classified under twelve different
headings according to their definition by power series, generating functions, infinite products, repeated differentiations, indefinite integrals, definite integrals, differential equations, difference equations, functional
equations, trigonometric series, series of orthogonal functions, or integral equations. Tables of definite integrals representing each function and numerical tables of a few new functions were to form part of the "Guide". An extensive table of definite integrals and a Guide to numerical tables of special functions were planned as companion works.https://resolver.caltech.edu/CaltechAUTHORS:20140123-104529738Tables of Integral Transforms
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Year: 1954
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.https://resolver.caltech.edu/CaltechAUTHORS:20140123-101456353