2
votes
0answers
27 views

Closed-form solution to polynomials of this special form?

I have two sets of real numbers $\{a_k\}$ and $\{b_k\}$ such that: $$a_n \leq \ldots \leq a_1 < b_1 \leq \ldots \leq b_n$$ Now consider the following polynomial equation: $$\prod_{k=1}^n (x - ...
3
votes
2answers
124 views

Closed form for $\prod_{1 \leq i < j \leq k} (j - i)$?

Is there a closed form for $\prod_{1 \leq i < j \leq k} (j - i)$? It looks like something like a determinant of a Vandermonde matrix, but I can't seem to get it to fit.
2
votes
2answers
752 views

Partial Sum of a Polynomial [duplicate]

Possible Duplicate: why is $\sum\limits_{k=1}^{n} k^m$ a polynomial with degree $m+1$ in $n$ I'm searching for a way to find the partial sum of a polynomial, is there any way of doing this ...