Bateman Manuscript Project
Encyclopedia
The Bateman Manuscript Project was a major effort at collation and encyclopedic compilation of the mathematical theory of special functions
. It resulted in the eventual publication of five important reference volumes, under the editorship of Arthur Erdélyi
.
The theory of special functions was a core activity of the field of applied mathematics
, from the middle of the nineteenth century to the advent of high-speed electronic computing. The intricate properties of spherical harmonics
, elliptic function
s and other staples of problem-solving in mathematical physics
, astronomy
and right across the physical sciences, are not easy to document completely, absent a theory explaining the inter-relationships. Mathematical table
s to perform actual calculations needed to mesh with an adequate theory of how functions could be transformed into those already tabulated.
Harry Bateman
, 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, who renewed them in the early 1980s. Dover
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 (see References).
Other mathematicians involved in the project include Wilhelm Magnus
.
Special functions
Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, functional analysis, physics, or other applications....
. It resulted in the eventual publication of five important reference volumes, under the editorship of Arthur Erdélyi
Arthur Erdélyi
Arthur Erdélyi FRS, FRSE was a Hungarian-born British mathematician. Erdélyi was a leading expert on special functions - especially orthogonal polynomials and hypergeometric functions.-Biography:...
.
The theory of special functions was a core activity of the field of applied mathematics
Applied mathematics
Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge...
, from the middle of the nineteenth century to the advent of high-speed electronic computing. The intricate properties of spherical harmonics
Spherical harmonics
In mathematics, spherical harmonics are the angular portion of a set of solutions to Laplace's equation. Represented in a system of spherical coordinates, Laplace's spherical harmonics Y_\ell^m are a specific set of spherical harmonics that forms an orthogonal system, first introduced by Pierre...
, elliptic function
Elliptic function
In complex analysis, an elliptic function is a function defined on the complex plane that is periodic in two directions and at the same time is meromorphic...
s and other staples of problem-solving in mathematical physics
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
, astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
and right across the physical sciences, are not easy to document completely, absent a theory explaining the inter-relationships. Mathematical table
Mathematical table
Before calculators were cheap and plentiful, people would use mathematical tables —lists of numbers showing the results of calculation with varying arguments— to simplify and drastically speed up computation...
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
Harry Bateman FRS was an English mathematician.-Life and work:Harry Bateman first grew to love mathematics at Manchester Grammar School, and in his final year, won a scholarship to Trinity College, Cambridge. There he distinguished himself in 1903 as Senior Wrangler and by winning the Smith's Prize...
, a distinguished applied mathematician, undertook the somewhat quixotic
Quixotism
Quixotism is impracticality in pursuit of ideals, especially those ideals manifested by rash, lofty and romantic ideas or extravagantly chivalrous action. It also serves to describe an idealism without regard to practicality...
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, who renewed them in the early 1980s. Dover
Dover Publications
Dover Publications is an American book publisher founded in 1941 by Hayward Cirker and his wife, Blanche. It publishes primarily reissues, books no longer published by their original publishers. These are often, but not always, books in the public domain. The original published editions may be...
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 (see References).
Other mathematicians involved in the project include Wilhelm Magnus
Wilhelm Magnus
Wilhelm Magnus was a mathematician. He made important contributions in combinatorial group theory, Lie algebras, mathematical physics, elliptic functions, and the study of tessellations....
.