The symbolic and numerical computational capabilities of the Maple system concerning special functions are constantly evolving. The requirements concerning mathematical functions, however, are not just computational: typically, you also need information on identities, alternative definitions, and mathematical properties in general. This leads to the idea of a FunctionAdvisor command and MathematicalFunctions project, where the main goals are

to provide tools for elementary and advanced algebraic and numerical computing with mathematical functions,

to make the information about mathematical functions that the Maple system can provide more complete with each release, while providing access to each piece of information through a simple interface.

The information on mathematical functions can be accessed directly from the Maple prompt, using the top-level FunctionAdvisor command. This functionality can be particularly useful when studying, teaching, or solving problems where mathematical function properties are relevant.

The advanced level achieved in combining symbolic and numerical computation also made possible the implementation of sophisticated mathematical functions, as is the case of the Heun and doubly hypergeometric Appell functions. Developments like these require a flexible numerical evaluation environment for performing experimentation with numerical methods. For this purpose, the MathematicalFunctions project provides the Evalf package.

Each command in the MathematicalFunctions package can be accessed by using either the long form or the short form of the command name in the command calling sequence. The FunctionAdvisor command can be used directly without invoking the MathematicalFunctions package.

The long form, MathematicalFunctions:-command, is always available. The short form can be used after loading the package.

The following is a list of available commands.

To display the help page for a particular MathematicalFunctions command, see Getting Help with a Command in a Package.

Cheb-Terrab, E.S. "The function wizard project: A Computer Algebra Handbook of Special Functions." Proceedings of the Maple Summer Workshop, University of Waterloo, Ontario, Canada, 2002.

Olver, F.W.J.; Lozier, D.W.; Boisvert, R.F.; Clark, C.W.; "NIST Handbook of Mathematical Functions." Cambridge University Press, 2010.

The MathematicalFunctions package was updated in Maple 2015.