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 The University of Western Australia (CRICOS Provider No 00126G) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul