tea.mathoverflow.net - Discussion Feed (Factorial series)

Mariano comments on "Factorial series" (18000)

Mariano — Sun, 08 Jan 2012 19:47:48 -0800

http://www.wolframalpha.com/input/?i=sum+n!%2F%28%282^%28n-1%29%29%282n-1%29!%29

j2m comments on "Factorial series" (17985)

j2m — Sat, 07 Jan 2012 20:10:13 -0800

Yes it can; a little bird told me that your series is equal to $\frac18\left(4+5\sqrt[8]{e}\sqrt{2\pi}\mathrm{erf}\left(\frac1{\sqrt{8}}\right)\right)$.

As for this being a good MO query, well...

Vassilis Parassidis comments on "Factorial series" (17984)

Vassilis Parassidis — Sat, 07 Jan 2012 14:38:34 -0800

During my work on particular functions I came up with the following: n!/[(2^{n-1})(2n-1)!]
As n takes values from 1 to infinity the sum converges to a limit that I cannot express in a closed form. Does anyone have an idea whether this limit can be expressed in a closed form?

If this, in its present form, is not a good MO question, how can I improve it?