All Questions
3
questions
4
votes
2
answers
462
views
Show that a polynomial vanishes
When doing the expansion of the following polynomial expression, the result is zero.
\begin{align*}
&- 1 (-1 - 2 x) (0 - 2 x) (1 - 2 x) (2 - 2 x) \\
&+5 (-1 - 1 x) (0 - 1 x) (1 - 1 x) (2 - 1 x)...
- 3,716
3
votes
2
answers
133
views
General form of the coefficients of the polynomial $p(z)=\binom{q+z}{n}+\binom{q-z}{n}$
In my mathematical wanderings I found this polynomial in $z$
$$
p(z)=\binom{q+z}{n}+\binom{q-z}{n}
$$
Now , I'm wondering what the general terms for the coefficients are. First of all its easy to see ...
- 5,627
3
votes
3
answers
542
views
Stirling Binomial Polynomial
Let $\{\cdot\}$ denote Stirling Numbers of the second kind. Let $(\cdot)$ denote the usual binomial coefficients. It is known that $$\sum_{j=k}^n {n\choose j} \left\{\begin{matrix} j \\ k \end{matrix}\...
- 3,251