# Tagged Questions

For questions about the evaluation of finite products, or their properties. For infinite ones, use "infinite-products" tag.

15 views

63 views

### Factorial Representation of product

So I've been trying to work out if it is possible to write: $\large \Pi_{i=1}^n (3i-1)$ as an expression involving the quotient or product of two factorials, or really any expression involving ...
20 views

### Product of a matrix and a tensor

I need to know how to compute the following product: $M(x)\frac{\partial M(x)}{\partial x}M(x)$ $\quad$ where $x \in R^{n}$. Assuming the dimensions of the matrices are compatible,how do we take ...
56 views

### Prove $\prod\limits_{k=0}^{n-1} \left(x^2-2x\cos \left(\alpha+\frac{2k\pi}{n}\right)+1\right)=x^{2n}-2x^n\cos(n\alpha)+1$

I have read in a paper that there is a formula as follows: $$\prod_{k=0}^{n-1} \left(x^2-2x\cos\left(\alpha+\frac{2k\pi}{n}\right)+1\right)=x^{2n}-2x^n\cos(n\alpha)+1.$$ In the paper they said that we ...
30 views

### Simplifying a -1 term out of a finite product

I've come up with an algorithm that relies upon the value of the following product: $$Q_{k} =\prod_{n=0}^k [f(n) - 1]$$ Where $f(n) \ge 2$ and strictly increasing integer function [see note]. ...
I am curious to know whether the following holds or not. If $n_1,n_2,n_3,m_1,m_2$ are positive integers strictly greater than 1 such that $$n_1+n_2+n_3 > m_1 +m_2$$ then $$n_1n_2n_3 \geq m_1m_2.$$ ...