SIAM AG on Orthogonal Polynomials and Special Functions


Extract from OP-SF NET

Topic #2   ------------   OP-SF NET 4.5  ------------ September 15, 1997
From: Willard Miller (
Subject: Report on Stanford Minisymposium "Handbooks for Special
             Functions and the World Wide Web"

The Activity Group on Orthogonal Polynomials and Special Functions
sponsored the Minisymposium "Handbooks for Special Functions and the World
Wide Web" that was held on July 14, 1997 at the SIAM Annual Meeting at
Stanford University. The principal handbooks on special 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consulted technical volumes ever published, but they are now out of date,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.
The minisymposium was organized by Dick Askey and Willard Miller, and
featured talks by representatives of the groups that are proposing to
update the Bateman Project (Mourad Ismail) and Abramowitz & Stegun (Dan
Lozier), respectively, a presentation on the development of a Mathematica
Special Functions Handbook (Oleg Marichev and Paul Wellin), and an
assessment of the historical influence of special functions handbooks
(Dick Askey), followed by a general discussion.

Willard Miller chaired the session and started with some desirable
criteria for handbooks: 1) Present, codify and organize the principal
results and tools in appropriate parts of the field of special functions.
Provide insight into the structure of the theory. 2)  Provide easy
accessibility for users. 3) Ensure long term impact. Do carefully
(accurately) and guided by the most knowledgeable experts in the field.
Make easy to update. 

Dan Lozier talked about the planning for publication on the World Wide Web
of a modernized and updated revision of the NBS Handbook of Mathematical
Functions, first published in 1964. The authoritative status of the
original publication is to be preserved by enlisting the aid of qualified
mathematicians and scientists. However, there will be increased practical
emphasis on formulas, graphs and numerical evaluation through the
provision of interactive capability to permit generation of tables and
graphs on demand. The "handbook" will be available at a Web site and will
involve a digital library. 
(Editor's Note: See Topic #6 below
for further information on this project.)

Mourad Ismail discussed plans for updating the Bateman project, both to
reflect progress made on topics covered in the original (written in the
early 1950's) and to add topics of current importance that were not in the
initial project. In particular, the plan is for major additions on one and
multi-variable orthogonal polynomials and on q-series. Mourad emphasized
the importance of involving leading experts in the project. The plan is
that the update should be published in a paper version, with formulas (and
corrections)  available via ftp or on a Web site. One of the arguments
that he presented for a paper version was that many third world
mathematicians and users of mathematics would not have access to a
Web-based product. Cambridge University Press has shown interest in the
project and some funding has been received from the National Security
Agency. Major funding is being sought from the National Science

Oleg Marichev presented current work on the Mathematica Interactive
Special Functions Handbook. The Wolfram Research representatives
emphasized the importance of using recent Web-based technological
developments in a handbook project. Their concept was to have a paper
version of the handbook and a World Wide Web version. On the Web version
search engines could be used, formulas could be down-loaded, manipulated
with Mathematica, and data could be generated and plotted. Hyperlinks
could be used to link formulas with the original reference where they are
derived. Updating and correcting would be simple on the Web. Their message
was that the Mathematica system should be used as the underlying system
for an update of either the NBS or the Bateman project. 

Dick Askey talked about the influence, for good or ill, of special
function handbooks through the decades. Many of his examples illustrated
the value of involving leading researchers in these projects. Their input
is critical in deciding what material to include and how to present it. 

The issued raised at the Minisymposium are of importance for all in the
special functions user community. The need for updating and codifying the
principal results of the theory are clear, but the sources of funding and
the optimal delivery system are not yet determined. Clearly, special
function handbooks will continue to be produced. If the special functions
research community is to have much influence on their content, we need to
resolve these issues now. 

Willard Miller, Jr.

Back to Home Page of
SIAM AG on Orthogonal Polynomials and Special Functions
Page maintained by Martin Muldoon