After more than 10 years, the U.S. Commerce Department's National Institute of Standards and Technology (NIST) has released the Digital Library of Mathematical Functions (DLMF) and its printed companion, the NIST Handbook of Mathematical Functions, highly anticipated updates to the agency's most widely cited publication. These modernized reference works contain a comprehensive set of mathematical tools useful for specialists who work with mathematical modeling and computation.
The works include a complete update and expansion of the 1964 Handbook of Mathematical Functions edited by NIST's Milton Abramowitz and Irene Stegun, which became an indispensable reference for scientists and engineers who use applied mathematics in their work. The 1964 volume sold an estimated one million copies and still averages more than 1,600 citations per year in scientific papers; NIST embarked on the new work in response to advances in electronic information exchange as well as in mathematics itself.
The new 36-chapter work is designed to be the definitive reference work on special functions in applied mathematics — a term used to describe the most important and widely employed mathematical functions. Special functions appear whenever natural phenomena are studied, engineering problems are formulated, and computer simulations are performed. The DLMF provides critical reference information needed to use these functions in practice, such as their precise definitions, alternative ways to represent them mathematically, illustrations of how the functions behave at extreme values, and their relationships to other functions and concepts.
The online DLMF, available free of charge, includes visual aids that provide qualitative information on the behavior of mathematical functions, such as interactive tools for rotating and zooming in on 3D representations. Clicking on an equation symbol leads to its definition. The DLMF also provides references to or hints for the proofs of all mathematical statements, offers advice on methods for computing mathematical functions, and provides active links to available software and references. The DLMF features a powerful search engine and is available at dlmf.nist.gov.