On Wed, Feb 14, 2024 at 6:12 PM Oscar Benjamin <oscar.j.benja...@gmail.com>
wrote:
> Maxima's simplify_sum function produces something similar looking:
>
> (%i4) load("simplify_sum");
> (%o4) "/usr/share/maxima/5.45.1/share/solve_rec/simplify_sum.mac"
>
> (%i5) sum(1/factorial(n^2), n, 1, inf), simpsum;
> (%o5) 'sum(1/(n^2)!,n,1,inf)
>
> (%i6) simplify_sum(%);
>
Oh, I see - I missed an explicit call to simplify_sum.
1/'product(n^2+%,%,1,2*n+1) non-rational term ratio to nusum
> 1/'product(n^2+%,%,1,2*n+1) non-rational term ratio to nusum
> (%o6) %f[1,4]([1],[1-%i,%i+1,1-sqrt(2)*%i,sqrt(2)*%i+1],1)
>
It seems to be a bug in simplify_sum() - nusum can't do it ( "non-rational
term ratio to nusum")
indeed, it's obvious that the sum is not hypergeometric, as the consequent
terms ratio is not of the right type,
so it does try something more clever - but fails.
Dima
>
> --
> Oscar
>
> On Wed, 14 Feb 2024 at 17:52, Dima Pasechnik <dimp...@gmail.com> wrote:
> >
> > It appears to come from Maxima, but I have trouble reproducing this in
> Maxima.
> > Perhaps it's a bug in the Maxima interface?
> > Is there a direct way to see how Maxima is called in this instance?
> >
> > Dima
> >
> >
> > On Mon, Feb 12, 2024 at 2:53 PM Georgi Guninski <ggunin...@gmail.com>
> wrote:
> >>
> >> There is discussion about this on mathoverlow [1]:
> >>
> >> The closed form of `sum(1/factorial(n**2),n,1,oo)` doesn't appear
> >> correct and it contradicts numerical computations, including
> verification
> >> with mpmath.
> >>
> >> Session:
> >>
> >> sage: import mpmath
> >> sage: su4=sum(1/factorial(n**2),n,1,oo);su4
> >> hypergeometric((1,), (-I + 1, I + 1, -I*sqrt(2) + 1, I*sqrt(2) + 1), 1)
> >> sage: CC(su4)
> >> 1.17227289255719 - 7.88860905221012e-31*I
> >> sage: mpmath.hyper((1,), (-I + 1, I + 1, -I*sqrt(2) + 1, I*sqrt(2) +
> 1), 1)
> >> mpc(real='1.1722728925571919', imag='-6.9025329206838533e-31')
> >> sage: su5=sum(1/factorial(i**2) for i in range(1,100))
> >> sage: CC(su5)
> >> 1.04166942239864
> >>
> >> sage: mpmath.nsum(lambda n: 1/mpmath.gamma(1+n**2),[1,mpmath.inf])
> >> mpf('1.0416694223986369')
> >>
> >>
> >> [1]:
> https://mathoverflow.net/questions/463964/factorial-series-jd-sum-n-1-infty-frac1nd-and-hypergeometric-fu
> >>
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