12 Aug
2010
12 Aug
'10
10:17 a.m.
On Thu, Aug 12, 2010 at 6:11 AM, Fred lunnon <fred.lunnon@gmail.com> wrote:
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!
Maple 13 passes:
sum(p!*q!*r!*j!/(p+q+r+j)!,j=0..infinity); (p + q + r) factorial(p) factorial(q) factorial(r) -------------------------------------------------- (p + q + r - 1) factorial(p + q + r)