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All New Visualizations Section

A major enhancement to this site has recently been made.

At its introduction in 2002, the site had 37,000+ formulas. With this enhancement, nearly 50,000 formulas and 11,000 graphics have been added to the original collection. This endeavor has been aided by a grant from the National Science Foundation.

Major areas with added identities include:

  • Indefinite integrals of elementary functions (approximately 18,000 identities)
    The website is now the largest collection of such integrals, and it is much more detailed than any existing handbook.
  • Transformations of inverse trigonometric functions (approximately 20,000 identities)
    The twelve tightly connected inverse trigonometric functions, due to the their branch cuts, comprise a rich set of identities. For more than 2000 such identities involving the inverse sine function, see http://functions.wolfram.com/ElementaryFunctions/ArcSin/27/02.

Additions have also been made throughout all functions and categories. Some never before published identities involve differential equations for Jacobi elliptic functions with respect to the modulus (see, for instance, http://functions.wolfram.com/EllipticFunctions/JacobiCN/13/01/01/0001/).

The visualization galleries for all elementary function have been completed, and the galleries for the mathematical constants are under construction. Detailed plots of the functions along the real axis, over the complex plane, differential equation, etc. are available for all elementary functions. The complete Mathematica source code for all visualizations is downloadable.

This recent enhancement to the Wolfram Function Site has also given an overall facelift to the site, including a new front page and a new look and feel.

A variety of further additions and enhancements reflect the comments and contributions that have been received by members of the mathematics and science community. One especially notable improvement is the inclusion of references (e.g., http://functions.wolfram.com/EllipticFunctions/JacobiCN/16/06/0001).