Tagged Questions
5
votes
2answers
298 views
How was Euler able to create an infinite product for sinc by using its roots?
In the Wikipedia page for the Basel problem, it says that Euler, in his proof, found that
$$\begin{align*}
\frac{\sin(x)}{x} &=
\left(1 - \frac{x}{\pi}\right)\left(1 + \frac{x}{\pi}\right)\left(1 ...
2
votes
2answers
113 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.
1
vote
1answer
160 views
Efficient calculation of polynomial product
I have 2 polynomials $p_1(x_1,\ldots,x_n)$ and $p_2(x_1,\ldots,x_n)$, of which I have to compute the product, with a special property: The exponent of each variable is always either $0$ or $1$, where ...
