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 Arthur Erdélyi FRS, FRSE (2 October 1908 – 12 December 1977) was a Hungarian-born British mathematician. Erdélyi was a leading expert on special functions, particularly orthogonal polynomials and hypergeometric functions. Biography He ...

Overview

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

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

, 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. Since the spherical harmonics form a ...

elliptic function In the mathematical field of complex analysis, elliptic functions are a special kind of meromorphic functions, that satisfy two periodicity conditions. They are named elliptic functions because they come from elliptic integrals. Originally those in ...

s and other staples of problem-solving in

mathematical physics Mathematical physics refers to 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 t ...

astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...

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 called the "physical sciences". Definition Phy ...

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

, a distinguished applied mathematician, undertook the somewhat

quixotic Quixotic may refer to: * Quixotism, deriving from the novel ''Don Quixote'' * ''Quixotic'' (album), an album by Martina Topley-Bird * Quix*o*tic Quix*o*tic was a rock band active from 1997 to 2002 in the area of Washington, D.C., United States. T ...

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 or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...

, who renewed them in the early 1980s.

Dover Dover () is a town and major ferry port in Kent, South East England. It faces France across the Strait of Dover, the narrowest part of the English Channel at from Cap Gris Nez in France. It lies south-east of Canterbury and east of Maidstone ...

planned to reprint them for publication in 2007, but this never occurred . 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 (February 5, 1907 in Berlin, Germany – October 15, 1990 in New Rochelle, New York) was a German-American mathematician. He made important contributions in combinatorial group theory, Lie algebr ...

, Fritz Oberhettinger and

Francesco Tricomi Francesco Giacomo Tricomi (5 May 1897 – 21 November 1978) was an Italian people, Italian mathematician famous for his studies on mixed type partial differential equations. He was also the author of a book on integral equations. Biography Trico ...

Askey–Bateman project

In 2007, the ''Askey–Bateman project'' was announced by

Mourad Ismail Mourad E. H. Ismail (born April 27, 1944, in Cairo, Egypt) is a mathematician working on orthogonal polynomials and special functions. Ismail received his bachelor's degree from Cairo University. He holds Masters and doctorate degrees from the U ...

as a five- or six-volume encyclopedic book series on special functions, based on the works of

and

Richard Askey Richard Allen Askey (4 June 1933 – 9 October 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 t ...

. Starting in 2020,

Cambridge University Press Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press A university press is an academic publishing hou ...

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 Tom H. Koornwinder (born 19 September 1943, in Rotterdam) is a Dutch mathematician at the Korteweg-de Vries Institute for Mathematics who introduced Koornwinder polynomials. See also * Askey–Bateman project The Bateman Manuscript Project was ...

Jasper V. Stokman Jasper, an Aggregate (geology), aggregate of microgranular quartz and/or cryptocrystalline chalcedony and other mineral phases,Kostov, R. I. 2010. Review on the mineralogical systematics of jasper and related rocks. – Archaeometry Workshop, 7, ...

) * 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 was the first female President of the American Association for the Advancement of Science (1971) and head of the mathematics department of the Office of Na ...

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

in 1981.); Reprint: Robert E. Krieger Publishing Co., Inc., Melbourne, Florida, USA. 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, USA. 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, USA. 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 , editor1-first=Diego , editor1-last=Dominici , editor2-first=Martin , editor2-last=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 , publisher=

, last1=Assche , first1=Walter Van , 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=

, 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