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Re: recognizing integer numbers

Mathematica cannot expand expressions like (a+b)^m or conversely, factor 
expand expressions into this form, even if you "tell it" that m is an 
integer. You can only do this sort of thing for a fixed non-negative 
integer m, like, say. m=20.


Simplify[Sum[Binomial[2*m + 1, k]*(a^k*b^(2*m + 1 - k) + b^k*a^(2*m + 
1 - k)), {k, 0, m}]]

(a + b)^41

Andrzej Kozlowski
Toyama International University

On Tuesday, April 23, 2002, at 08:13  PM, manuel ballester wrote:

> 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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