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Published 1953 | Erratum + Published
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Higher Transcendental Functions [Volumes I-III]


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.

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. The California Institute of Technology wishes to express its thanks both to the family of the late Professor Bateman for the gift of his notes and of his library, and to the Office of Naval Research and especially to Dr. Mina Rees, the Director of its Mathematical Sciences Division, 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 following persons and organizations: to Professor Michal for his preliminary survey of Bateman's notes; to the University of Edinburgh for granting leave of absence to Dr. Erdélyi; to the Rockefeller Foundation for defraying travelling expenses for Dr. and Mrs. Erdélyi on their visit in 1947-48; to the University of Turin for granting leave of absence to Professor Tricomi; to Professors T. M. Apostol of the California Institute, R. C. Archibald of Brown University, E. D. Rainville of the University of Michigan, Mr. S. O. Rice of the Bell Telephone Laboratories, and Professor C. A. Truesdell of Indiana University for information or consultations in connection with the work; and to the McGraw-Hill Company for technical advice and publication. Last but not least, acknowledgments should be expressed to Dr. Erdélyi and the staff of the Bateman Manuscript Project for the faithful and highly competent performance of a difficult task.

Attached Files

Published - Volume_1.pdf

Published - Volume_2.pdf

Published - Volume_3.pdf

Erratum - Errata-volume2.pdf

Erratum - Errata.pdf


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August 19, 2023
October 25, 2023