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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