|
Elementary and special mathematical functions play a significant role in
mathematics, the natural sciences, engineering, and other fields. These
functions were an important aspect of Mathematica when it was
originally designed, and they continue to be significant as Mathematica
evolves. Among all existing software programs, Mathematica
has the most complete numeric and symbolic implementation of mathematical
functions. At the same time, the world of special mathematical functions is
far too complex to be completely represented in a single computer program.
Literature on special functions has been available for some time. However,
the vast majority of special function literature predates the computer
mathematics age, thus having its limitations. The Wolfram Functions
Site was developed to address these limitations and to provide the
scientific community with a valuable resource.
The site was designed to be similar in nature to existing handbooks that
detail special mathematical functions, but there are a number of
differences between the Wolfram Functions Site and these handbooks.
- The site is designed to be easy, straightforward, efficient, and
also expandable as more material becomes available. No prior knowledge
of Mathematica is required to take advantage of the material on the
site.
- Contributions from researchers are welcome to
help expand the scope of the site.
- The site is based on Mathematica notebook technology that
enables
the automatic generation of different presentation media. Current formats
include HTML, PDF, and Mathematica notebooks.
In its current form, this site is the result of three
years of
work. Future updates for the Wolfram Functions Site include:
- Creating a Mathematica package that allows the conversion of
various identities into interactively applicable rules inside a
Mathematica session
- Adding tables of data for time-consuming calculations, such as the
zeros of Zeta and PrimePi for large arguments
- Enabling interactive numeric evaluation and plotting using webMathematica
technology
- Creating Mathematica programs for generating an arbitrary number
of terms for a series expansion where no closed forms are known, such as
the zeros of Airy functions and the Taylor series for Mathieu functions
- Adding special functions currently not implemented in
Mathematica,
such as various totient functions, Dedekind sums, Kelvin functions, Fox's
H-function, and hypergeometric and Meijer G functions of several
variables
- Specifying formulas that are correct for all functions of a given
class
- Adding detailed reference and historical information
- Noting important applications of the various functions
- Adding special tutorials, overviews, summaries, and
state-of-the-art reports about various function groups and individual
special functions
|
