I made a diagram based on one by Adam Majewski on wikicommons. Turns out the `betaF` code on the mu-ency page is way faster than the earlier code on the page. This image with 1000 terms calculated in a fraction of the time of 500 terms used in the previous post. Seems to take roughly O(n log n) space (discounting the growth of the numbers stored..).
I'm using my memo-sqlite #haskell package to memoize the series coefficients in a database, persisted between program invocations, so I don't have to wait 30mins each time.
Then I convert and pack the list of Rational from the db into an unboxed Vector Double, for faster series evaluation at each point of the curve (using Horner's rule).