Preface

[This preface was written for the original release of the DLMF in 2010. For an up-to-date account of the current status of the project, see About the Project.]

The NIST Handbook of Mathematical Functions, together with its Web counterpart, the NIST Digital Library of Mathematical Functions (DLMF), is the culmination of a project that was conceived in 1996 at the National Institute of Standards and Technology (NIST). The project had two equally important goals: to develop an authoritative replacement for the highly successful Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, published in 1964 by the National Bureau of Standards (M. Abramowitz and I. A. Stegun, editors); and to disseminate essentially the same information from a public website operated by NIST. The new Handbook and DLMF are the work of many hands: editors, associate editors, authors, validators, and numerous technical experts. A summary of the responsibilities of these groups may help in understanding the structure and results of this project.

Executive responsibility was vested in the editors: Frank W. J. Olver (University of Maryland, College Park, and NIST), Daniel W. Lozier (NIST), Ronald F. Boisvert (NIST), and Charles W. Clark (NIST). Olver was responsible for organizing and editing the mathematical content after receiving it from the authors; for communicating with the associate editors, authors, validators, and other technical experts; and for assembling the Notations section and the Index. In addition, Olver was author or co-author of five chapters. Lozier directed the NIST research, technical, and support staff associated with the project, administered grants and contracts, together with Boisvert compiled the Software sections for the Web version of the chapters, conducted editorial and staff meetings, represented the project within NIST and at professional meetings in the United States and abroad, and together with Olver carried out the day-to-day development of the project. Boisvert and Clark were responsible for advising and assisting in matters related to the use of information technology and applications of special functions in the physical sciences (and elsewhere); they also participated in the resolution of major administrative problems when they arose.

The associate editors are eminent domain experts who were recruited to advise the project on strategy, execution, subject content, format, and presentation, and to help identify and recruit suitable candidate authors and validators. The associate editors were:

• Richard A. Askey, University of Wisconsin-Madison

• Michael V. Berry, University of Bristol

• Walter Gautschi, (resigned 2002), Purdue University

• Leonard C. Maximon, The George Washington University

• Morris Newman, The University of California, Santa Barbara

• Ingram Olkin, Stanford University

• Peter Paule, Johannes Kepler University

• William P. Reinhardt, University of Washington

• Nico M. Temme, Centrum Wiskunde & Informatica

• Jet Wimp, (resigned 2001), Drexel University

The technical information provided in the Handbook and DLMF was prepared by subject experts from around the world. They are identified on the title pages of the chapters for which they served as authors and in the table of Contents.

The validators played a critical role in the project, one that was absent in its 1964 counterpart: to provide critical, independent reviews during the development of each chapter, with attention to accuracy and appropriateness of subject coverage. These reviews have contributed greatly to the quality of the product. The validators were:

• Tom M. Apostol, California Institute of Technology

• Antony Ross Barnett, University of Waikato

• Alexander I. Bobenko, Technische Universität Berlin

• B. L. J. Braaksma, University of Groningen

• David M. Bressoud, Macalester College

• Bille C. Carlson, Iowa State University

• Bernard Deconinck, University of Washington

• T. Mark Dunster, San Diego State University

• Amparo Gil, Universidad de Cantabria

• Alexander A. Its, Indiana University

• Brian R. Judd, The Johns Hopkins University

• Roelof Koekoek, Delft University of Technology

• Tom H. Koornwinder, Universiteit van Amsterdam

• Robb J. Muirhead, Pfizer Global R&D

• Edward Neuman, Southern Illinois University at Carbondale

• Adri B. Olde Daalhuis, The University of Edinburgh

• Richard B. Paris, University of Abertay Dundee

• Ranjan Roy, Beloit College

• Simon Ruijsenaars, University of Leeds

• Javier Segura, Universidad de Cantabria

• René F. Swarttouw, Vrije Universiteit, Amsterdam

• Nico M. Temme, Centrum Wiskunde & Informatica (CWI)

• Hans Volkmer, University of Wisconsin–Milwaukee

• Gerhard Wolf, University of Duisberg-Essen

• Roderick S. C. Wong, City University of Hong Kong

All of the mathematical information contained in the Handbook is also contained in the DLMF, along with additional features such as more graphics, expanded tables, and higher members of some families of formulas; in consequence, in the Handbook there are occasional gaps in the numbering sequences of equations, tables, and figures. The Web address where additional DLMF content can be found is printed in blue at appropriate places in the Handbook. The home page of the DLMF is accessible at DLMF.

The DLMF has been constructed specifically for effective Web usage and contains features unique to Web presentation. The Web pages contain many active links, for example, to the definitions of symbols within the DLMF, and to external sources of reviews, full texts of articles, and items of mathematical software. Advanced capabilities have been developed at NIST for the DLMF, and also as part of a larger research effort intended to promote the use of the Web as a tool for doing mathematics. Among these capabilities are: a facility to allow users to download LaTeX and MathML encodings of every formula into document processors and software packages (eventually, a fully semantic downloading capability may be possible); a search engine that allows users to locate formulas based on queries expressed in mathematical notation; and user-manipulable 3-dimensional color graphics.

Production of the Handbook and DLMF was a mammoth undertaking, made possible by the dedicated leadership of

• Bruce R. Miller, Information Technology Editor, NIST

• Bonita V. Saunders, Visualization Editor, NIST

• Abdou Youssef, Mathematics and Search Indexing, George Washington University and NIST

Miller was responsible for information architecture, specializing LaTeX for the needs of the project, translation from LaTeX to MathML, and the search interface. Saunders was responsible for mesh generation for curves and surfaces, data computation and validation, graphics production, and interactive Web visualization. Youssef was responsible for mathematics search indexing and query processing. They were assisted by the following NIST staff: Marjorie A. McClain (LaTeX, bibliography), Joyce E. Conlon (bibliography), Gloria Wiersma (LaTeX), Qiming Wang (graphics generation, graphics viewers), and Brian Antonishek (graphics viewers).

The editors acknowledge the many other individuals who contributed to the project in a variety of ways. Among the research, technical, and support staff at NIST these are B. K. Alpert, T. M. G. Arrington, R. Bickel, B. Blaser, P. T. Boggs, S. Burley, G. Chu, A. Dienstfrey, M. J. Donahue, K. R. Eberhardt, B. R. Fabijonas, M. Fancher, S. Fletcher, J. Fowler, S. P. Frechette, C. M. Furlani, K. B. Gebbie, C. R. Hagwood, A. N. Heckert, M. Huber, P. K. Janert, R. N. Kacker, R. F. Kayser, P. M. Ketcham, E. Kim, M. J. Lieberman, R. R. Lipman, M. S. Madsen, E. A. P. Mai, W. Mehuron, P. J. Mohr, S. Olver, D. R. Penn, S. Phoha, A. Possolo, S. P. Ressler, M. Rubin, J. Rumble, C. A. Schanzle, B. I. Schneider, N. Sedransk, E. L. Shirley, G. W. Stewart, C. P. Sturrock, G. Thakur, S. Wakid, and S. F. Zevin. Individuals from outside NIST are S. S. Antman, A. M. Ashton, C. M. Bender, J. J. Benedetto, R. L. Bishop, J. M. Borwein, H. W. Braden, C. Brezinski, F. Chyzak, J. N. L. Connor, R. Cools, A. Cuyt, I. Daubechies, P. J. Davis, C. F. Dunkl, J. P. Goedbloed, B. Gordon, J. W. Jenkins, L. H. Kellogg, C. D. Kemp, K. S. Kölbig, S. G. Krantz, M. D. Kruskal, W. Lay, D. A. Lutz, E. L. Mansfield, G. Marsaglia, B. M. McCoy, W. Miller, Jr., M. E. Muldoon, S. P. Novikov, P. J. Olver, W. C. Parke, M. Petkovsek, W. H. Reid, B. Salvy, C. Schneider, M. J. Seaton, N. C. Severo, I. A. Stegun, F. Stenger, M. Steuerwalt, W. G. Strang, P. R. Turner, J. Van Deun, M. Vuorinen, E. J. Weniger, H. Wiersma, R. C. Winther, D. B. Zagier, and M. Zelen. Undoubtedly, the editors have overlooked some individuals who contributed, as is inevitable in a large long-lasting project. Any oversight is unintentional, and the editors apologize in advance.

The project was funded in part by NSF Award 9980036, administered by the NSF’s Knowledge and Distributed Intelligence Program. Within NIST financial resources and staff were committed by the Information Technology Laboratory, Physics Laboratory, Systems Integration for Manufacturing Applications Program of the Manufacturing Engineering Laboratory, Standard Reference Data Program, and Advanced Technology Program.

Notwithstanding the great care that has been exercised by the editors, authors, validators, and the NIST staff, it is almost inevitable that in a work of the magnitude and scope of the NIST Handbook and DLMF errors will still be present. Users need to be aware that none of these individuals nor the National Institute of Standards and Technology can assume responsibility for any possible consequences of such errors.

Lastly, the editors appreciate the skill, and long experience, that was brought to bear by the publisher, Cambridge University Press, on the production and publication of the new Handbook.

Frank W. J. Olver

Editor-in-Chief and Mathematics Editor

Daniel W. Lozier

General Editor

Ronald F. Boisvert

Information Technology Editor

Charles W. Clark

Physical Sciences Editor