Mathematical functions reference released

After a decade of preparation, the US Commerce Department's National Institute of Standards and Technology has released the Digital Library of Mathematical Functions and its printed companion, the NIST Handbook of Mathematical Functions.

These modernised reference works contain a comprehensive set of mathematical tools useful for any and all specialists who work with mathematical modelling and computation.

The works comprise a complete update and expansion of the 1964 Handbook of Mathematical Functions.

The 36-chapter tome is designed to be the definitive reference work on applied mathematics ‘special functions’. Special functions appear whenever natural phenomena are studied, engineering problems are formulated and computer simulations are performed. They also are in statistics, financial models and economic analysis.

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.

"When studying a phenomenon, experts want to know more than just how to describe it qualitatively," says NIST's Dan Lozier, one of the works' editors. "They need to know its relationships to other phenomena and get insight into its behaviour. For this they need mathematics. And as they progress with their research, whether it is in mathematics, science or engineering, they want to know how to perform all the necessary mathematical analyses and computations, from conception to conclusion. The DLMF will help with all these tasks."

The new work includes information about additional special functions that have come to prominence in applied mathematics, the physical sciences and engineering, as well as in other fields.

The online DLMF includes visual aids that provide qualitative information on the behaviour of mathematical functions, such as interactive tools for rotating and zooming in on three-dimensional representations. These visualisations can be explored with free browsers and plug-ins for PC, Mac and Linux systems.

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. It also features a powerful search engine.

"This is a much more complete package for the user," Lozier says. "We anticipate the DLMF to be a useful resource for everyone who has benefited from the 1964 publication, and expect that it will find new audiences among biologists, data security specialists and every other branch of science that employs computer-based models."