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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




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