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Value of finite sum

  1. Jan 18, 2008 #1

    I came across a somewhat unwieldy sum which I do not know how to manipulate any further. I suspect it might have something to do with a hypergeometric series, but I am not sufficiently familar with those series to be able to just see how it might be related to them.

    The sum in question is

    [tex]\sum_{1\leq r_1< r_2 < \dots < r_n \leq m}{\frac{ (k-1)!!(k-2r_1)!!(k-2r_2+1)!! \dots (k-2r_{n-1}+n-2)!!(k-2r_n+n-1)!! }{ (k-2r_1+1)!!(k-2r_2+2)!! \dots (k-2r_{n-1}+n-1)!!(k-2r_n+n)!! }}[/tex]

    where k is some non-negative integer, [tex]0\leq n \leq k[/tex]. m is defined by

    [tex]m=\left\lfloor\frac{k+n}{2}\right\rfloor \geq n[/tex].

    Do you know of any books where I could look up things like that?

    Any help is greatly appreciated.

    Last edited: Jan 18, 2008
  2. jcsd
  3. Jan 19, 2008 #2


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  4. Jan 26, 2008 #3
    Thanks. A=B seems to be an intersting book, I hadn't heard of it before.
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