# Questions tagged [products]

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

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### Is it possible to extract the sum of products without having the individual values?

Consider two sequences A and B. They have the same size. I can calculate any individual statistics from either of them, like averages, products, summations, etc. However, because they are very large, ...
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### A summation involving the inverses of the products of the elements of subsets of a set

A big thank you in advance to all who have sacrificed their time to help me with the following problem. Consider a set $T$ containing the first $k$ natural numbers. First, we find all the $v$-...
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### closed form for $\prod_{k=0}^{n}\left(1-2\alpha \cos\frac{2\pi k}{n}\right)$

Does anybody know a closed form for this multiplication? $$\prod_{k=0}^{n}\left(1-2\alpha \cos\frac{2\pi k}{n}\right)$$ where $\alpha$ is a real number or maybe even a potential method to use to ...
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### Calculate the product: $(\sin\frac{\pi}{12} + i\cos\frac{\pi}{12}) (\sin\frac{\pi}{6} + i\cos\frac{\pi}{6}) (\sin\frac{\pi}{4} + i\cos\frac{\pi}{4})$

Calculate the following product: $$\left(\sin\frac{\pi}{12} + i\cos\frac{\pi}{12}\right) \left(\sin\frac{\pi}{6} + i\cos\frac{\pi}{6}\right) \left(\sin\frac{\pi}{4} + i\cos\frac{\pi}{4}\right)$$ ...
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### How do I make a $\prod$ function explicit?

I've got a $\prod$ (product operator) function that I'm trying to make explicit. I've managed to convert everything else to explicit form, which we can call $g(x)$, except for this one part, so ...
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### Does $\prod_{m=1}^\infty \frac{1}{m^2}$ have a closed form?

We know that $$\sum_{m=1}^\infty \frac{1}{m^2} = \frac{\pi^2}{6},$$ but what about the product of the reciprocal of the squares: $$\prod_{m=1}^\infty \frac{1}{m^2}?$$ Do we use a different product ...
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### Any example of measurable spaces where the measurable rectangles form an algebra on the product space?

As far as I know, for any $(\Omega_{i},\sigma_{i})$ i=1,2, $\textit{A}=\{A_{1}\times A_{2}: A_{1}\in\sigma_{1}, A_{2}\in\sigma_{2}\}$ is not an algebra in general on $\Omega_{1}\times\Omega_{2}$ in ...
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### Is $\prod\limits_{p}{p^\frac{1}{p}}$ convergent?

I am trying to prove or disprove if $\prod\limits_{p}{p^\frac{1}{p}}$ converges. I have tested up to 400K and got the following value: $$\prod_{p}{p^\frac{1}{p}}=0.26431187257195837519$$ while for ...
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### Quotient of cartesian product by the right action of a group

I've been recently reading about Burnside rings and I found Serge Bouc's paper. In one of its sections he explains different kinds of functors that will be considered in further reasoning. I got stuck ...
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### How to check if a number can be represented as product of 2 consecutice numbers?

How to check if a number can be represented as product of 2 consecutice numbers? Eg 56 can be represented since 56 = 7*8 72 can be represented since 72 = 8*9