Re: Finite Sum
- To: mathgroup at smc.vnet.net
- Subject: [mg44537] Re: Finite Sum
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Thu, 13 Nov 2003 05:57:55 -0500 (EST)
- Organization: The University of Western Australia
- References: <bovefl$kt3$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <bovefl$kt3$1 at smc.vnet.net>,
Ratna Bandila <choppalaks at yahoo.com> wrote:
> Kindly help if anyone has come across the Finite Sum
> expression and has found the closed-form formula for
>
> Sum[(2*(n-m))!/(m!^2*(n-m)!^4),{m,0,n}]
If you enter this expression into Mathematica it automatically returns a
closed-form formula in terms of a (terminating) generalized
hypergeometric function. In general, this will not simplify any further.
If you reverse the summation order, you do get a slightly simpler
result, again in terms of a generalized hypergeometric function:
Sum[(2*(n - m))!/(m!^2*(n - m)!^4) /. m -> n - m, {m, 0, n}]
HypergeometricPFQ[{1/2, -n, -n}, {1, 1}, 4]/Gamma[n + 1]^2
Cheers,
Paul
--
Paul Abbott Phone: +61 8 9380 2734
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