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MathGroup Archive 2003

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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
School of Physics, M013                         Fax: +61 8 9380 1014
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Crawley WA 6009                      mailto:paul at physics.uwa.edu.au 
AUSTRALIA                            http://physics.uwa.edu.au/~paul


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