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flintlib / arb

Arb has been merged into FLINT -- use https://github.com/flintlib/flint/ instead
http://arblib.org/
GNU Lesser General Public License v2.1
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More combinatorial sequences (wishlist) #261

Open videlec opened 5 years ago

videlec commented 5 years ago

K. Brigmann developed analogues of Rademacher formula for many other integral sequences. It is tempting to write certified numerical algorithms for evaluating them.

Ideally, there should exist a compiler that would turn modularity properties of generating function into a certified algorithm for numerical evaluation of the coefficients.

fredrik-johansson commented 5 years ago

I agree, I had the idea for such compiler years ago but the details are beyond me :)

fredrik-johansson commented 2 years ago

Before I forget about this issue again: I did the j-function coefficients in https://github.com/fredrik-johansson/jfunction

Turns out, it is difficult to do it purely numerically because proving Rademacher-like tight error bounds is a nightmare. But the hybrid modular-numerical algorithm should generalize really well.