- #1
Pere Callahan
- 582
- 1
Hi,
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
\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)! }}
where k is some non-negative integer, 0\leq n \leq k. m is defined by
m=\left\lfloor\frac{k+n}{2}\right\rfloor \geq n.
Do you know of any books where I could look up things like that?
Any help is greatly appreciated.
-Pere
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
\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)! }}
where k is some non-negative integer, 0\leq n \leq k. m is defined by
m=\left\lfloor\frac{k+n}{2}\right\rfloor \geq n.
Do you know of any books where I could look up things like that?
Any help is greatly appreciated.
-Pere
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