Definitive Mathematical Functions Site Now Available
January 7, 2004--87,160 formulas and 10,828 graphics about mathematical
functions are now available free at The Wolfram Functions
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
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
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."