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MathGroup Archive 2002

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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


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