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1. The project needs texinfo documentation.
2. There needs to be more tests and more tests for factorial_simp.
3. Maybe the code should be re-written in Common Lisp. This wouldn't make it faster or particularly better. But it would make it easier to put into the Maxima core.

Extensions

1. The code could be extended to do similar kinds of simplifications with the digamma function; see for example, https://dlmf.nist.gov/5.5.E4 .