How is this type of polynomial $\prod_{i}^N (x-i)$ called? $N$ is an arbitrary integer.
Is there a well-known property? It would be nice to get to know that.
Asked
Active
Viewed 61 times
1
-
falling factorial – achille hui Nov 12 '18 at 08:45
-
@achillehui Sorry, how is that related? – user Nov 12 '18 at 08:51
-
@gimusi The falling factorial $(x)n = \prod{k=1}^n (x-k+1)$. The polynomial at hand is simply $(x-1)_N$. – achille hui Nov 12 '18 at 08:56
1 Answers
0
It is the unique monic polynomial wih degree $N$ and exactly $N$ integer roots $x=1,2,\ldots,N$.
user
- 154,566