Wolfram Archive

# Definitive Mathematical Functions Site Now Available

Published January 7, 2004

January 7, 2004–87,160 formulas and 10,828 graphics about mathematical functions are now available free at The Wolfram Functions Site.

Created using Mathematica over the course of more than a decade by mathematical functions experts at Wolfram Research, The Wolfram Functions Site is an important new resource for mathematicians, scientists, engineers, and students.

Elementary mathematical functions, such as sine and cosine, are familiar to anyone who has taken high school mathematics, but in the applications of mathematics to science and engineering–as well as in pure mathematics itself–there are also several hundred so-called “special functions” that have been intensively used for a century or more.

These special functions–with names like Bessel functions, hypergeometric functions, and totient functions–define focal points of mathematical knowledge. If a problem can be solved in terms of, say, a Bessel function, then this immediately means that accumulated knowledge about Bessel functions can be applied. The Wolfram Functions Site provides in a readily accessible way the largest collection, by far, of such knowledge ever assembled.

With early precursors dating back to the 1500s, several widely used handbooks of mathematical functions appeared in book form in the period from 1920-1970. The largest of these contained about 15,000 formulas, meticulously compiled from thousands of technical papers.

Today, with Mathematica, new systematic methods–many developed at Wolfram Research specifically for this project–allow vast numbers of additional formulas to be found and tested. The Wolfram Functions Site assembles all of these formulas and makes them immediately accessible for human or computer use.

Says Michael Trott, leader of the project, “The Wolfram Functions Site is the first true semantic website in which a substantial area of human knowledge has been completely encoded in a form that can be not only read but also actually understood by a computer. It defines important foundations for many developments to come.”

Traditional handbooks of mathematical functions contained handfuls of graphics illustrating the properties of functions. With Mathematica, a huge number of new visualizations of functions have become possible. The Wolfram Functions Site assembles over 10,000 of these, with many more being planned.

A major tour de force of web reference development, The Wolfram Functions Site contains over 30 gigabytes of data. Its creation was made possible by a new generation of automated website construction technology based on Mathematica symbolic documents.

Material in The Wolfram Functions Site can be downloaded in several standard formats, including Mathematica InputForm and StandardForm, MathML, and PDF. Each formula has been assigned a unique permanent ID that can be used by documents in which the formula is cited. Formulas can be copied from the site and immediately used as input to a computer system.

The Wolfram Functions Site is part of a constellation of major technical public-information web resources provided by Wolfram Research. Another Wolfram web resource is MathWorld–the most visited mathematics site on the web. Both MathWorld and The Wolfram Functions Site are partially supported by the National Science Foundation under its Digital Library Initiative.

While having already far surpassed previous knowledge bases for mathematical functions, continued growth is planned for The Wolfram Functions Site, with new searching capabilities, external contributions, and new classes of graphics and information.

Says The Wolfram Functions Site team member Oleg Marichev, one of the world’s most recognized special functions experts, “Having previously spent 18 years writing integral tables by hand, I am both amazed and honored to have participated in creating this site. Mathematica has enabled us to encapsulate and share this mathematical knowledge in a truly comprehensive, active way.”