4 Prospectus

A reference work like the NBS Handbook can be made even more valuable by putting it on the WWW. This theme has been explored, with attention paid to obstacles as well as opportunities.

The basic content of the handbook is found in the Mathematical Properties sections of the core chapters. A well-funded project to revise the handbook will provide the opportunity to update these sections to take account of mathematical developments of the last 30-plus years. For example, the chapter on elliptic integrals predates the influential work of Carlson that not only supplanted the standard functions of Legendre with more satisfactory symmetric functions but also yielded effective algorithms that are now found in virtually all computer libraries of special functions. And there have been important developments in discrete orthogonal polynomials, basic and generalized hypergeometric functions, and q-functions that are not covered at all in the existing handbook. We plan to follow the proven success of Abramowitz's approach: contract with key mathematicians who can do a first-rate job of writing the chapters of the new handbook, under the supervision of a carefully selected panel of senior research mathematicians and scientists who have a proven record of accomplishment with respect to special functions. We plan to add to this approach a very strong validation process, supervised by the same panel, in which the chapters are peer-reviewed independently of the authors. Independent validation was not a feature of the original handbook project but was used, for example, with great success in the later development of the NAG Library⁶. Additional informal reviews and comments from the mathematical and scientific community at large will provide still further validation.

We envision a concentrated effort over a 2-3 year period, after which the initial stage of the handbook revision project will be complete. This period will begin upon receipt of adequate funding authority. The initial stage will cover all the existing handbook, with extensions, but not with standard reference software substituted for standard reference tables. The second stage is in some ways already started through its connection to the Software Test Service for Special Functions. However, much research and development is needed before an acceptable standard library for the numerical generation of special functions can be constructed. Therefore the second stage will undoubtedly continue well beyond the completion of the initial stage.

Footnotes

... Library⁶

B. Ford and J.C.T. Pool, The Evolving NAG Library Service, in W.R. Cowell (Ed.), Sources and Development of Mathematical Software, Prentice-Hall, 1984, pp. 375-397.