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.
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
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.
All the help pages are available directly from within Maple, and here are pdf versions:
The gfun package itself.
Functions manipulating these expressions, starting with the most commonly used: diffeqtorec, rectodiffeq, algebraicsubs, poltodiffeq, poltorec, borel, cauchyproduct, diffeq+diffeq, diffeq*diffeq, diffeqtohomdiffeq, hadamardproduct, invborel, rec+rec, rec*rec, rectohomrec.
NumGfun has its own documentation.
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.