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
--
You received this message because you are subscribed to the Google Groups
"sage-devel" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to sage-devel+unsubscr...@googlegroups.com.
To view this discussion on the web visit
https://groups.google.com/d/msgid/sage-devel/CAGUWgD8FTWhurhrHbs5d_7DE0FL4f4bb_MCE6d7B%3DKZdsmC4Ew%40mail.gmail.com.
