The gfun package

Gfun is a Maple package that provides tools for

  • guessing a sequence or a series from its first terms;

  • manipulating rigorously solutions of linear differential or recurrence equations, using the equation as a data-structure.

Latest version

 gfun 3.84 (March 2021). Once downloaded, see the help page of libname to understand how to make them available from Maple. Typically, your session will contain something like libname:="gfun_path",libname:

You can check that this worked by asking gfun:-version(); that should return the number above.

The source code can be read by anyone who can read Maple code, but if you want to use the package, then it’s better to download it with the link above.

Help pages

All the help pages are available directly from within Maple, and here are pdf versions:

Reference for gfun

The primary reference to use when citing gfun is the following one:

B. Salvy and P. Zimmermann, “Gfun: a Maple package for the manipulation of generating and holonomic functions in one variable,” ACM Transactions on Mathematical Software, vol. 20, no. 2, pp. 163–177, 1994.

If you are using the NumGfun subpackage, then the proper reference is:

M. Mezzarobba, “NumGfun: a Package for Numerical and Analytic Computation with D-finite Functions,” in Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation (ISSAC 2010), 2010, pp. 139–145.

Articles citing gfun

There are many of them. I used to maintain a list, but it is much easier to point directly to the corresponding page on Google Scholar.