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 datastructure.
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:

The gfun package itself.

Functions converting expressions to differential or algebraic equations: algfuntoalgeq, algeqtodiffeq, holexprtodiffeq.

Functions extracting information from these representations: algeqtoseries, ratpolytocoeff, rectoproc. See also the standard DEtools and LREtools Maple packages, and the NumGfun subpackage.

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.

Functions for guessing: listtodiffeq, listtorec, listtoalgeq, listtoratpoly, listtohypergeom, guessgf, seriestodiffeq, seriestorec, seriestoalgeq, seriestoratpoly, seriestohypergeom.

NumGfun has its own documentation.

Functions related to continued fractions: the ContFrac subpackage, riccati_to_cfrac, expr_to_cfrac, examples from the Handbook of Continued Fractions.
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 Dfinite 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.