recognizing integer numbers

*To*: mathgroup at smc.vnet.net*Subject*: [mg33924] recognizing integer numbers*From*: manuel_ballester at yahoo.com (manuel ballester)*Date*: Tue, 23 Apr 2002 07:13:50 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Dear All: I need some help with the following. I am trying mathematica to solve some sums for me. The thing is that I don't know how to tell mathematica that certain numbers are non-negative integers and some answers that I would expect as (for example) n! are given as Gamma[n-1] and so on, sometimes Hypergeometric functions are also involved. Example: Sum[Binomial[2*m+1,k]*( a^k*b^(2*m+1-k)+ b^k*a^(2*m+1-k) ),{k,0,m}] if m is a natural number then the answer to this is simply (a+b)^(2*m+1) but since I don't know how to say this to mathematica it gives me an answer with gamma and hypergeometric functions. I already tried Simplify and FullSimplify. Thanks for your help manuel