The National Institute of Standards and Technology (NIST) has released a five-chapter preview of the highly anticipated online Digital Library of Mathematical Functions (DLMF). In development for more than a decade, the DLMF is designed to be a modern successor to the 1964 Handbook of Mathematical Functions, one of the most cited works in mathematical literature. The preview of the new DLMF is a fully functional beta-level release of five of the 36 chapters.

The DLMF is designed to be the definitive reference work on the special functions of applied mathematics — “special” because they occur frequently in mathematical modeling of physical phenomena, from atomic physics to optics and water waves. These functions have also found applications in many other areas, such as 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 DLMF also provides visual aids to provide qualitative information on the behavior of mathematical functions, including interactive Web-based tools for rotating and zooming in on 3D representations. These 3D 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 DLMF goes to an entire page on the function.

The complete DLMF will 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 version. A print edition will also be published. The DLMF, being compiled and edited at NIST, received seed money from the National Science Foundation and contributions of more than 50 subject experts worldwide. The preview can be accessed at dlmf.nist.gov.