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Jul 26, 2011 at 12:36 comment added Joe Silverman The formula is trivial, just reverse the order of summation and use the binomial theorem twice. What makes you think that your series will have a simple closed expression. Most series don't.
Jul 26, 2011 at 9:10 comment added David Thanks for the answer! I can't see how you have this result though... However, I kind need a closed expression for $A_{m,n}(x)$ because I would need to take an expectation on $n$ (which is random)! Would you know where I could possibly find the answer? I have been looking for identities involving the generalization of falling factorials but I couldn't find any litterature...
Jul 25, 2011 at 15:44 history answered Joe Silverman CC BY-SA 3.0