Workshop Focuses on NIST Mathematical Digital Library Project
August 2002
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.
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Lind Hall at the University of Minnesota, home of the IMA.
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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.
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Associate Editors review DLMF chapters at Editorial meeting held in conjunction
with the IMA Workshop. From left to right:
Frank Olver,Charles Clark, Ingram Olkin, Michael Berry, Walter Gautschi, Daniel Lozier,
Nico Temme, William Reinhardt, Peter Paule, Richard Askey.
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