If I'm interpreting the formula right, the separation of P,Q,R is a smokescreen. It could be simplified to the subproblem "sum of J!/(N+J)!", which ought to be in the toolbox of any symbolic math system. Rich ________________________________________ From: math-fun-bounces@mailman.xmission.com [math-fun-bounces@mailman.xmission.com] On Behalf Of Fred lunnon [fred.lunnon@gmail.com] Sent: Thursday, August 12, 2010 4:11 AM To: math-fun Subject: [math-fun] sums of reciprocal multinomials Here's something which may be as new to some other people on the list as it was to me, though it must surely be well-known (and probably has some connection to do with those ghastly hypergeometric series that I keep trying to avoid). I illustrate with the tetranomial case --- the generalisation to any dimension is obvious: \sum_{0<=j<oo} p!q!r!j!/(p+q+r+j)! = p!q!r!/(p+q+r-1)(p+q+r-1)! Does anyone know of a reference for these and similar results --- for example, generalisation to summation over several indices? Can Mathematica, Macsyma etc. deduce them --- Maple 9 flunked! This was brought to my attention by an enquiry from a physicist: not only did I have to admit that I didn't recognise it, but neither could I tell him where to go look for it. Fred Lunnon _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun