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Is this question acceptable?: Factorial series

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    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?
    • CommentAuthorj2m
    • CommentTimeJan 7th 2012
     

    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...

    • CommentAuthorMariano
    • CommentTimeJan 8th 2012
     

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

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