IMA 2002 Summer Program:

Special Functions in the Digital Age

July 22 - August 2, 2002

Organizers:
 

Mathematical tables and handbooks have played a pivotal role in applications and also the development of mathematics itself over the centuries.  Now, with the advent of the digital age, the traditional handbook format has become obsolete, and a complete rethinking of the nature and role of mathematical handbooks must be undertaken.  The purpose of this program is to formulate, though concrete examples and experiences, the role and character of digital libraries in mathematics, and the mathematical and applied fields that would benefit from such a library.  The first serious attempt to address these issues is the ongoing Digital Library of Mathematical Functions (DLMF) project at the National Institute of Standards and Technology (NIST).  This workshop will take the DLMF project as a basis for assessing both the state of the art in special function theory, what aspects are of importance in applications, particularly to chemistry and physics, and the experiences gained in this project to formulate recommendations for how digitial libraries of mathematics should be organized, utilized, and developed.  We also anticipate the experiences of the DLMF project to provide insight and recomendations for how mathematics should be stored and disseminated over the internet.

Of the currently used handbooks, the most well-developed have been those devoted to special functions and their applications.  The principal handbooks on special functions, "Higher Transcendental Functions" (the Bateman Project) and the NIST (formerly National Bureau of Standards) "Handbook of Mathematical Functions," are among the most useful, widely consulted technical volumes ever published, but they are now out of date, due to rapid research progress and revolutionary changes in technology.  (See http://www.siam.org/siamnews/03-98/function.htm for additional information.) Using these as concrete examples of a mathematical digital library, the program will assess recent progress in updating these handbooks and recent advances in the theory and use of special functions, and to point out the areas of research in special functions that hold the most promise and importance for future development, both for theorists and users.  In the broader arena, the workshop will aim to use the experience in this particular subject to generate recommendations for further digital library projects in the mathematical sciences and their applications, including, but not limited to, numerical analysis, group theory, signal processing, statistics, linear algebra, partial differential equations, and so on.

See an article by Peter Paule on the DLMF project.

Description:

The  IMA workshop will use the DLMF project as a foundation and discuss what more should be done, what areas are incomplete or unrepresented, what are the resulting mathematical, symbolic, numerical and web issues, applications in physics, chemistry, etc., relationships with the Bateman project, and potential for other digital libraries in other mathematical areas. The workshop is to have a very broad outlook, encompassing a wide range of subjects connected with special functions, as well as issues concerning digital libraries and the delivery of mathematics over the internet.

A major portion of this program (7 days) will be assessments of  research progress and promising vistas for future research by distinguished experts in the areas of  asymptotics,  combinatorial functions, statistics, computer algebra, algebraic and group theoretic methods, applications to the physical sciences,  orthogonal polynomials, numerical methods, zeta functions   &  random matrices,  Painlevé functions, elliptic functions,  elliptic hypergeometric functions and the Heun function group, with the aim of pointing out what is of greatest importance in the theory and applications, and what should be included in digital library projects.

The remainder of the program (3 days) will be devoted to Digital Libraries generally and, specifically, Digital Libraries and the Mathematical Sciences, including the delivery of mathematics over the Internet. It will conclude with a panel  on  the "Future of Mathematical Digital Libraries," with panelists from the special functions research and users communities, as well as representatives from mathematics societies and government funding agencies.

There will be several discussion sessions to develop specific recommendations for special function topics to be included in future Digital Libraries in Mathematics.  Also there will be poster sessions, and several software demonstrations (particularly of computer algebra and numerical packages for special functions), and much of the software will be available during the program for informal use by participants. This program will link with special function related sessions at the Foundations of Computational Mathematics (FoCM'02) meeting that will be hosted by the IMA, August 5-15, 2002.

The program is meant for researchers in the theory and computation of special functions (definitely including people new to the field who are looking for the most promising areas for future research), for users of special functions, and for persons interested in the delivery of mathematics over the Internet.