Excellent, thank you.
>PS. This is essentially using the recursive definition given
>in Wikipedia. Wikipedia calls this inefficient, but AFAICS
>due to memoization it is much better than Akiyama-Tanigawa
>presented in Wikipedia.
I read several papers on the Bernoulli function. Axiom references
John Brillhart's "On the Euler and Bernoulli polynomials" which
was his Berkeley PhD thesis but I can't find a copy online anywhere.
There were a couple papers which were an efficiency contest between
Mathematica and Sage. Sage uses Pari's implementation by default
which gives excellent results. Pari uses
\[ |B_n| = \frac{2n!}{(2\pi)^n}\zeta(n) \]
with floats but you have to completely control the precision.
Wolfram published
http://blog.wolfram.com/2008/04/29/today-we-broke-the-bernoulli-record-from-the-analytical-engine-to-mathematica
Sage claims that bernoulli(10^5) takes about 11 seconds.
Tim
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