The Bateman Manuscript Project was a major effort at collation and encyclopedic compilation of the mathematical theory of

special functions Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. The term is defined by ...

. It resulted in the eventual publication of five important reference volumes, under the editorship of Arthur Erdélyi.

Overview

The theory of special functions was a core activity of the field of

applied mathematics Applied mathematics is the application of mathematics, mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and Industrial sector, industry. Thus, applied mathematics is a ...

, from the middle of the nineteenth century to the advent of high-speed electronic computing. The intricate properties of

spherical harmonics In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations in many scientific fields. The table of spherical harmonics co ...

elliptic function In the mathematical field of complex analysis, elliptic functions are special kinds of meromorphic functions, that satisfy two periodicity conditions. They are named elliptic functions because they come from elliptic integrals. Those integrals are ...

s and other staples of problem-solving in

mathematical physics Mathematical physics is the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the de ...

astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...

and right across the

physical sciences Physical science is a branch of natural science that studies non-living systems, in contrast to life science. It in turn has many branches, each referred to as a "physical science", together is called the "physical sciences". Definition ...

, are not easy to document completely, absent a theory explaining the inter-relationships.

Mathematical table Mathematical tables are lists of numbers showing the results of a calculation with varying arguments. Trigonometric tables were used in ancient Greece and India for applications to astronomy and celestial navigation, and continued to be widely u ...

s to perform actual calculations needed to mesh with an adequate theory of how functions could be transformed into those already tabulated.

Harry Bateman Harry Bateman FRS (29 May 1882 – 21 January 1946) was an English mathematician with a specialty in differential equations of mathematical physics. With Ebenezer Cunningham, he expanded the views of spacetime symmetry of Lorentz and Poinca ...

, a distinguished applied mathematician, undertook the somewhat quixotic task of trying to collate the content of the very large literature. On his death in 1946, his papers on this project were still in a uniformly rough state. The publication of the edited version provided special functions texts more up-to-date than, for example, the classic Whittaker & Watson. The volumes were out of print for many years, and copyright in the works reverted to the

California Institute of Technology The California Institute of Technology (branded as Caltech) is a private research university in Pasadena, California, United States. The university is responsible for many modern scientific advancements and is among a small group of institutes ...

, who renewed them in the early 1980s. In 2011, the California Institute of Technology gave permission for scans of the volumes to be made publicly available. Other mathematicians involved in the project include

Wilhelm Magnus Hans Heinrich Wilhelm Magnus, known as Wilhelm Magnus (5 February 1907 in Berlin, Germany – 15 October 1990 in New Rochelle, New York), was a German-American mathematician. He made important contributions in combinatorial group theory, Lie algeb ...

, and Francesco Tricomi.

Askey–Bateman project

In 2007, the ''Askey–Bateman project'' was announced by Mourad Ismail as a five- or six-volume encyclopedic book series on special functions, based on the works of

and

Richard Askey Richard Allen Askey (June 4, 1933 – October 9, 2019) was an American mathematician, known for his expertise in the area of special functions. The Askey–Wilson polynomials (introduced by him in 1984 together with James A. Wilson) are on the ...

. Starting in 2020,

Cambridge University Press Cambridge University Press was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessme ...

began publishing volumes 1 and 2 of this ''Encyclopedia of Special Functions'' with series editors Mourad Ismail and : * Volume 1: Univariate Orthogonal Polynomials (editor: Mourad Ismail) * Volume 2: Multivariable Special Functions (editors: Tom H. Koornwinder, Jasper V. Stokman) * Volume 3: Hypergeometric and Basic Hypergeometric Functions (editor: Mourad Ismail) Further volumes were considered to include topics such as: * Continued fractions, number theory, and elliptic and theta functions * Equations of mathematical physics, including continuous and discrete Painlevé, Lamé and Heun equations * Transforms and related topics

Bibliography

*

https://resolver.caltech.edu/CaltechAUTHORS:20140123-104529738] (xxvi+4 errata pages+302 pages, red cloth hardcover) (NB. With a preface by

Mina Rees Mina Spiegel Rees (August 2, 1902 – October 25, 1997) was an American mathematician. She is known for her assistance to the US Government during WWII, as well as making several breakthroughs for women in science. Her most notable accomplishment ...

and a foreword by Earnest C. Watson. Copyright was renewed by

in 1981.); Reprint: Robert E. Krieger Publishing Co., Inc., Melbourne, Florida, US. 1981. ; Planned Dover reprint . *

https://resolver.caltech.edu/CaltechAUTHORS:20140123-104529738] (xvii+1 errata page+396 pages, red cloth hardcover) (NB. Copyright was renewed by

in 1981.); Reprint: Robert E. Krieger Publishing Co., Inc., Melbourne, Florida, US. 1981. ; Planned Dover reprint: . *

https://resolver.caltech.edu/CaltechAUTHORS:20140123-104529738] (xvii+292+2 pages, red cloth hardcover) (NB. Copyright was renewed by

in 1983.); Reprint: Robert E. Krieger Publishing Co., Inc., Melbourne, Florida, US. 1981. ; Planned Dover reprint . *

(xx+391 pages including 1 errata page, red cloth hardcover) *

(xvi+451 pages, red cloth hardcover) * (1+6+111+1+1 pages) * (343 pages, cloth hardcover) * (327 pages, cloth hardcover)

References

{{Reflist, refs= {{cite news , title=The Askey-Bateman Project , author-first=Mourad E. H. , author-last=Ismail , author-link=Mourad E. H. Ismail , volume=14 , number=5 , id=Topic #7 , date=2007-09-15 , editor-first1=Diego , editor-last1=Dominici , editor-first2=Martin , editor-last2=Muldoon , newspaper=OP-SF NET: The Electronic News Net of the SIAM Activity Group on Orthogonal Polynomials and Special Functions , pages=9–10 , url=https://math.nist.gov/~DLozier/OPSFnet/OPSF-Net_14-5.pdf , access-date=2020-09-26 , url-status=live , archive-url=https://web.archive.org/web/20200707025602/https://math.nist.gov/~DLozier/OPSFnet/OPSF-Net_14-5.pdf , archive-date=2020-07-07 (23 pages) {{cite web , title=Askey–Bateman project , author-first=Tom H. , author-last=Koornwinder , author-link=Tom H. Koornwinder , date=2020 , url=https://staff.science.uva.nl/t.h.koornwinder/specfun/AskeyBateman.html , access-date=2020-09-26 , url-status=live , archive-url=https://web.archive.org/web/20201029110244/https://staff.science.uva.nl/t.h.koornwinder/specfun/AskeyBateman.html , archive-date=2020-10-29 {{cite book , title=Univariate Orthogonal Polynomials , volume=I , series=Encyclopedia of Special Functions: The Askey-Bateman project , editor-first1=Mourad E. H. , editor-last1=Ismail , editor-link1=Mourad E. H. Ismail , editor-first2=Walter , editor-last2=Van Assche , editor-link2=:nl:Walter Van Assche , date=September 2020 , edition=1 , isbn=978-0-52119742-7 , doi=10.1017/9780511979156 , oclc=1195045133 , lccn=2020007276, publisher=

, publication-place=New York, USA , s2cid=230669315 (xii+388 pages) {{cite book , title=Multivariable Special Functions , volume=II , series=Encyclopedia of Special Functions: The Askey-Bateman project , editor-first1=Tom H. , editor-last1=Koornwinder , editor-link1=Tom H. Koornwinder , editor-first2=Jasper V. , editor-last2=Stokman , editor-first3=Mourad E. H. , editor-last3=Ismail , editor-link3=Mourad E. H. Ismail , editor-first4=Walter , editor-last4=Van Assche , editor-link4=:nl:Walter Van Assche , date=2021 , orig-date=October 2020 , edition=1 , isbn=978-1-10700373-6 , doi=10.1017/9780511777165 , oclc=1226183178 , publisher=

, publication-place=New York, USA , s2cid=240874629 (xii+427 pages) Errata
https://web.archive.org/web/20201029110207/https://staff.science.uva.nl/t.h.koornwinder/art/2021/AskBatVol2_errata.pdf -->
/ref> Mathematics literature Special functions History of mathematics

Overview

Askey–Bateman project

See also

Bibliography

References