I've filed https://sourceforge.net/p/maxima/bugs/4262/
On Wed, Feb 14, 2024 at 7:14 PM Dima Pasechnik <dimp...@gmail.com> wrote:
>
>
> 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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