Topic #2 ------------ OP-SF NET 4.5 ------------ September 15, 1997 ~~~~~~~~~~~~~ From: Willard Miller (email@example.com) 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Mathematical Functions," are among the most useful, widely consulted technical volumes ever published, but they are now out of date, due to rapid research progress and revolutionary changes in technology.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 Foundation. 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.