Algorithms used for the generalized expansions

Most of algorithms are producing sequences once x is given. They can almost all be stated in terms of a 2 term recurrence.
x(0) is the initial value and y(n) are the terms of the sequence. Here is a list of the principal algorithms used, it is NOT an exhaustive list.

Classical algorithms

Egyptian fractions

Infinite products algorithms

Miscellaneous algorithms

In each of these cases, the GFUN program is used to reconstruct the generating function (if possible),
that generates the number.