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
> Simplify and FullSimplify.
>