Re: recognizing integer numbers

*To*: mathgroup at smc.vnet.net*Subject*: [mg33984] Re: [mg33924] recognizing integer numbers*From*: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>*Date*: Thu, 25 Apr 2002 03:00:05 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

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. In[1]:= m=20; In[2]:= Simplify[Sum[Binomial[2*m + 1, k]*(a^k*b^(2*m + 1 - k) + b^k*a^(2*m + 1 - k)), {k, 0, m}]] Out[2]= (a + b)^41 Andrzej Kozlowski Toyama International University JAPAN http://platon.c.u-tokyo.ac.jp/andrzej/ 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 > > >