A simpleton's way of getting out of the problem indeed. PARI/GP's
documentation says:
? ?bernvec
bernvec(n): returns a vector containing, as rational numbers, the Bernoulli
numbers B_0, B_2, ..., B_{2n}.
? bernfrac(3)
%2 = 0
? bernfrac(5)
%3 = 0
So not only B_1 but also B_3, B_5, etc. have values.
Jeremy Tan / Parcly Taxel
On Tuesday, 13 September 2022 at 15:03:05 UTC+8 vdelecroix wrote:
> PARI/GP actually has a better convention : only even Bernoulli numbers
> exist
>
> ? bernvec(5)
> %1 = [1, 1/6, -1/30, 1/42, -1/30, 5/66]
>
> And the two conventions can be recovered as evaluations of Bernoulli
> polynomials at 0 and 1 respectively
>
> ? [subst(bernpol(n), x, 0) | n <- [1..6]]
> %2 = [-1/2, 1/6, 0, -1/30, 0, 1/42]
> ? [subst(bernpol(n), x, 1) | n <- [1..6]]
> %3 = [1/2, 1/6, 0, -1/30, 0, 1/42]
>
> I second Edgar that I don't see much of the point on doing this
> change. If we had to do any change I would suggest to raise an error
> when bernoulli(n) is called with n=1 so that nobody could complain
> about sage convention choices.
>
> Vincent
>
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