Library of Math Functions Previews
 This visual representation of a Hankel function for complex variables in the DLMF can be explored in three dimensions by Web users. Hankel functions are solutions of Bessel's differential equation and they play an important role in many problems of mathematical physics, such as including heat conduction and wave propagation. Courtesy of NIST |
The National Institute of Standards and Technology (NIST) has released a five-chapter preview of the much-anticipated online
Digital Library of Mathematical Functions (
DLMF). In development for over a decade, the
DLMF is designed to be a modern successor to the 1964
Handbook of Mathematical Functions, a reference work that is the most widely distributed NIST publication with over a million copies in print. It is one of the most cited works in the mathematical literature, still receiving over 1,600 yearly citations in the research literature. The preview of the new
DLMF is a fully functional beta-level release of five of the 36 chapters.
The library is designed to be the definitive reference work on the special functions of applied mathematics. Special functions are considered “special” because they occur very frequently in mathematical modeling of physical phenomena, from atomic physics to optics and water waves. These functions also have found applications in many other areas like cryptography and signal analysis. The
DLMF provides basic information needed to use these functions in practice, such as their precise definitions, alternate ways to represent them mathematically, illustrations of how the functions behave with extreme values and relationships between functions.
The library provides various visual aids to provide qualitative information on the behavior of mathematical functions, including interactive Web-based tools for rotating and zooming in on three-dimensional representations. These 3-D visualizations can be explored with free browsers and plug-ins designed to work in virtual reality markup language (VRML). Mouse over any mathematical function, and the
DLMF provides a description of what it is; click on it, and the library goes to an entire page on the function. The
DLMF provides references to or hints for the proofs of all mathematical statements. It also provides advice on methods for computing mathematical functions, as well as pointers to available software.
The complete library, with 31 additional chapters providing information on mathematical functions from Airy to Zeta, is expected to be released in early 2009. With over 9,000 equations and more than 500 figures, it will have about twice the amount of technical material of the 1964 handbook. An approximately 1,000-page print edition that covers all of the mathematical information available online also will be published. The library is being compiled and extensively edited at NIST, and received initial seed money from the National Science Foundation. It represents contributions of more than 50 subject-area experts worldwide.
The
DLMF preview can be accessed at
dlmf.nist.gov.