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Question: Is this double sum over a binomial in error?

Question:Is this double sum over a binomial in error?

guyp 20 Maple
October 31 2014
3

 

Maple returns the wrong answer to the following very simple double sum:

T:=(x,m)->sum( sum(binomial(m,k+p),k=1..m-p)*x^p,p=0..m-1);

Maple gives zero for all m>0.  However, the correct answer is a non-zero polynomial in x. 

For example, with Maple:

T(x, 3);
                               0

The correct answer is  x^2+4*x+7.

It would be helpful if others can check this double sum in their version of Maple and report results.

 
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