I believe what is wanted is the sum of all pairs where :
There is a name for this, but it escapes me at the moment....
Hi, I'm reading the preliminary algebra section of 'Mathematical Methods for Physics and Engineering' and the book explain that for a polynomial
then
where
are the zeroes of the polynomial
Please can someone explain the summation term to me, I thjnk I have an idea what it means.
Can someone write out the summation explicitly in the case of n=3
Thanks
(The "k> j" doesn't makes sense as a lower bound on a sum. I assume it was k= j+1 so that k goes from j+ 1 to n, always being larger than j.)
means . Notice that the "inner sum" is in every term of the "outer sum".
If n= 5, that would be .
If n= 3, .
(I just noticed that my " " is you " ". Sorry about that.
For example, if , , and are the zeros of a cubic polynomial , then the polynomial can be factored as and multiplying that out gives . Notice that the coefficient of x is the sum of the products of two s and that coefficient was . That is, so .
You should be able to see that by multiplying , "sum of products of two s" is the coefficient of . That's why that sum is .