MathGroup Archive 2003

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Finite Sum

  • To: mathgroup at
  • Subject: [mg44537] Re: Finite Sum
  • From: Paul Abbott <paul at>
  • Date: Thu, 13 Nov 2003 05:57:55 -0500 (EST)
  • Organization: The University of Western Australia
  • References: <bovefl$kt3$>
  • Sender: owner-wri-mathgroup at

In article <bovefl$kt3$1 at>,
 Ratna Bandila <choppalaks at> 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


Paul Abbott                                   Phone: +61 8 9380 2734
School of Physics, M013                         Fax: +61 8 9380 1014
The University of Western Australia      (CRICOS Provider No 00126G)         
35 Stirling Highway
Crawley WA 6009                      mailto:paul at 

  • Prev by Date: Optimization with conditional restrictions
  • Next by Date: Re: Readability confuses mathematica?
  • Previous by thread: Finite Sum
  • Next by thread: NotebookFind using Previous or Next *without wrapping*?