Workshop Focuses on NIST Mathematical Digital Library Project
Eight ITL and PL staff members participated in a workshop on Special Functions in the Digital Age hosted by the Institute for Mathematics and Its Applications (IMA) at the University of Minnesota in Minneapolis from July 22-August 2, 2002. The workshop was inspired by the NIST Digital Library of Mathematical Functions (DLMF) project. About 80 researchers from 14 countries participated.
According to the call for participation,
"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 digital libraries of mathematics should be organized, utilized, and developed."
The DLMF is currently under development at NIST as an interactive Web-based information resource on the special functions of applied mathematics. The project is being undertaken by ITL in collaboration with the NIST Physics Lab, MEL's Systems Integration for Manufacturing Applications (SIMA) Program, TS's Standard Reference Data Program, and the National Science Foundation.
A major part of the workshop's program was devoted to the assessment of research progress and consideration of promising vistas for future research in (a) special functions, including combinatorial functions, orthogonal polynomials, the zeta function, elliptic functions, hypergeometric functions, statistical functions, PainlevÉ functions, Mathieu functions, LamÉ functions, and spheroidal wave functions, (b) analysis tools, including asymptotics, algebraic and group-theoretic methods, computer algebra, numerical methods and software, and (c) applications in the physical sciences. Speakers surveyed what is of greatest importance in theory and applications, and what should be included in digital library projects. The remainder of the program was devoted to the development of digital libraries in the mathematical sciences, including the delivery of mathematics over the Internet. Among the distinguished group of speakers at the workshop were most of the authors of the DLMF's 40 chapters, as well as members of the DLMF editorial board.
NIST participants (and the titles of their presentations) were as follows. From ITL: Ronald Boisvert (Building the DLMF: Information Technology Issues), Daniel Lozier (Development of a New Handbook and Web Site of Properties of Special Functions), Bruce Miller (Representation, Display and Manipulation of Mathematics on the Web), Frank Olver, guest researcher from the University of Maryland (Error Bounds, Hyperasymptotics, and Uniform Asymptotics), Bonita Saunders (Interactive 3D Visualizations of High Level Functions in a Mathematical Digital Library), and Abdou Youssef, faculty appointee from George Washington University (Search Systems for Mathematical Equations). From PL: Charles Clark and William Reinhardt, faculty appointee from the University of Washington (New and old addition theorems and Landen identities for Jacobian elliptic functions: do these indeed give rise to "novel" solutions for non-linear PDEs?).
The workshop was the IMA's featured summer program for 2002. The IMA is an NSF- sponsored center established to increase the impact of mathematics by fostering research of a truly interdisciplinary nature. The IMA's work is carried out through a sequence of thematic programs ranging in length from two weeks to ten months, involving hundreds of long-term, medium-term and short-term visitors, from academia, industry, and government.