4 Graphics and Visualization

A Web-based digital library offers significant advantages over printed media for the presentation of informative graphics. Whereas graphical representations in [1] were sparse and restricted to static 2D plots, in the DLMF, dynamic 3D visualizations of complex special functions will complement 2D and 3D still images. The judicious use of graphics not only will help scientists and other technical users gain a deeper understanding of special functions, it will also assist us in making some parts of the DLMF accessible to educators, students and others who want a short introduction to the field.

The development of effective graphical displays in the DLMF presents several challenges. To insure uniformity throughout the DLMF, we must come to a consensus about the location, frequency, and type of visualizations to be placed in the system; but close collaboration with individual authors will be required to determine the specific needs for each chapter. A reliable means of computing accurate data for the visualizations must be found, and the author must decide which special features of a function, such as zeros, poles, and other singularities, should be emphasized. At the same time, the plotting range and scaling of the function must be determined to illustrate best those features. Another issue is deciding the type of file formats to be used, while also considering the availability of any additional Web plug-ins that would be needed by the user. We address some of these challenges by examining what we have done for the chapter on Airy functions in the prototype Web site.