Introduction

One of the most well known publications to come out of the National Bureau of Standards, the predecessor organization of the National Institute of Standards and Technology (NIST), is the Handbook of Mathematical Functions [1], published in 1964. Unchanged since the tenth printing in 1972, it continues to be widely sold by the US Government Printing Office, Dover, and many other commercial publishers. The Science Citation Index indicates that the handbook was cited over 26,000 times during the period 1974-1997 in more than 1000 journals, and the number of citations continues to increase with time.

The continued interest in the handbook plus such factors as

• the clear advantages of electronic media for the construction and communication of ideas in technical fields;
• advances in basic mathematical and computational techniques associated with the classical special functions of the mathematical and physical sciences; and
• the identification of new functions having widespread importance in emerging applications

have led NIST to embark on a massive project to update and expand the current handbook and disseminate it in digital format on the World Wide Web; see Lozier [2] for an early description and http://dlmf.nist.gov/for current information on this new project. The new entity, which is being called the Digital Library of Mathematical Functions (DLMF), will make full use of advanced communications and computational resources. A key feature of the DLMF will be dynamic 3D visualizations of special functions that allow a user to conduct interactive explorations of the relationship between a function's mathematical or numerical properties and its graphical representations. The Virtual Reality Modeling Language (VRML) is a standard 3D file format for describing the behavior and geometry of a 3D virtual world, or scene. Its accessibility on the Internet and interactive capabilities make it an ideal candidate for this development work. This paper describes techniques we are using to generate VRML files that not only display 3D graphs, but also allow the user to gain a deeper understanding of the function by manipulating cutting planes perpendicular to the major axes in order to examine the 2D projection of the function at various locations.