by the way, mathematica gives Sum[ p!q!r!j!/(p+q+r+j)!, {j, 0, Infinity}] = (Gamma[1 + p] Gamma[1 + q] Gamma[1 + r])/((-1 + p + q + r)^2 Gamma[-1 + p + q + r]) note the squared factor in the denominator Bob Baillie --- Dan Asimov wrote:
Fred 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 . . .
Hmm, dividing both sides, one gets:
\sum_(0<=j<oo) j!/(k+j)! = 1/((k-1)(k-1)!)
--Dan
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