Peter Luschny's Bernoulli Manifesto (http://luschny.de/math/zeta/The-Bernoulli-Manifesto.html) makes a very convincing argument that bernoulli(1) should be +1/2, not -1/2. Knuth's books (e.g. here are his replacement pages for earlier that 34th editions of "Concrete Mathematics") now use +1/2, SymPy now uses +1/2 (and I made the PRs implementing that, see sympy/sympy#23926), and so this ticket sets bernoulli(1) = +1/2 here too.

Well not quite; this ticket merely deprecates bernoulli(1) = -1/2 by providing a flag enforcing +1/2 behaviour. The intention is to make the +1/2 behaviour default later on, so as to give time for end-users to update their code.

This is a continuation of the sage-devel thread at https://groups.google.com/g/sage-devel/c/G4sbKoibXK4.

CC: @fredrik-johansson @DavidAyotte @PeterLuschny @edgarcosta @asmeurer

Component: number theory

Keywords: bernoulli numbers

Author: Jeremy Tan Jie Rui

Branch/Commit: u/gh-Parcly-Taxel/bern1 @ b5ce7de

Issue created by migration from https://trac.sagemath.org/ticket/34521