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(%);
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)
--
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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