Upon request of folks from the zoom call, I posted some suggestions on github that I report here:
There is a standard for the class of numerical functions that are needed in scientific computation. Traditionally, that was for a long time the “blue book” *Handbook of Mathematical Functions", by Abramowitz and Stegun. However, the American National Institute of Standard and Technology (NIST) has sing long ago taken the burden on its shoulder. After countless years of work and revision, the new
Digital Library of Mathematical Functions (DLMF)
has been published.
The DLMF is a the perfect starting point to broaden the standard library. All formulas are tested, some are implemented, and all rigorously referenced and documented. So there is no better blueprint.
Anywhere would be good to start, but I suggest
- confluent hypergeometric functions
- legendre and related functions
- orthogonal polynomials
- Coulomb functions
- spherical-group coefficients (3j, 6j, 9j)
the Digital Library of Mathematical Functions (DLMF) is as authoritative and standard a reference as one can ever possibly get. My suggestion, therefore, would be to shape the special function libraries in terms of one module per DLMF chapter, and figure out which already existing libraries provide the functionalities.
That said, GAMS is a gem of a website, which I have used for over a decade 