List questions from products

Published on 21 Jan 2024 - 6:35

151

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For $J=\{1,2,\dots,n \}$ is there an easy way to compute $\prod\limits_{i\in J | i \ne k} (k-i)$?

Published on 25 Jan 2024 - 19:46

111

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Closed form for $(n^2+1^2)(n^2+2^2)...(n^2+(n-1)^2)$, $n\in\mathbb{N}$

Published on 06 Feb 2024 - 17:43

126

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Techniques for proving this series identity?

Published on 10 Feb 2024 - 23:56

234

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How to find the coefficient of $x^k$ in the expression $\prod_{p=1}^n (x^p+1)^p$?

Published on 12 Feb 2024 - 20:50

35

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Some pattern in the gap of the extrema/root of a product using Stirling approximation

Published on 16 Feb 2024 - 10:36

51

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Sums and Products over sets of sets

Published on 16 Feb 2024 - 17:55

183

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how to calculate $\sum\limits_{k=1}^{+\infty }{\arctan \frac{1}{1+k^{2}}}$

Published on 22 Feb 2024 - 14:05

48

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Prove $\frac{(n/2)!(n/2)!}{\left(\frac{n+i}2\right)!\left(\frac{n-i}2\right)!}=\prod_{j=1}^{i/2}\frac{\frac n2+1-j}{\frac n2+j}$

Published on 25 Feb 2024 - 17:45

1.6k

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Every matrix is a product of two symmetric matrices

Published on 26 Feb 2024 - 6:11

40

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Inequality with Products and Sums

Published on 26 Feb 2024 - 14:27

66

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Understanding Why a Product of Cyclic Groups with Non-Coprime Orders is not Cyclic

Published on 01 Apr 2026 - 4:25

64

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Is there an Euler-Maclaurin-like formula for products?

Published on 02 Mar 2024 - 11:14

63

Views

Maximum product of numbers that add up to 10?

Published on 06 Mar 2024 - 3:13

36

Views

Motivation and intuition behind the geometric product integral

Published on 09 Mar 2024 - 12:09

List Question

Solutions $X_{k}$ to the equation $\sum_{k=0}^N X_{k} (-2^k)^n = 1$

For $J=\{1,2,\dots,n \}$ is there an easy way to compute $\prod\limits_{i\in J | i \ne k} (k-i)$?

Closed form for $(n^2+1^2)(n^2+2^2)...(n^2+(n-1)^2)$, $n\in\mathbb{N}$

Techniques for proving this series identity?

How to find the coefficient of $x^k$ in the expression $\prod_{p=1}^n (x^p+1)^p$?

Some pattern in the gap of the extrema/root of a product using Stirling approximation

Sums and Products over sets of sets

how to calculate $\sum\limits_{k=1}^{+\infty }{\arctan \frac{1}{1+k^{2}}}$

Prove $\frac{(n/2)!(n/2)!}{\left(\frac{n+i}2\right)!\left(\frac{n-i}2\right)!}=\prod_{j=1}^{i/2}\frac{\frac n2+1-j}{\frac n2+j}$

Every matrix is a product of two symmetric matrices

Inequality with Products and Sums

Understanding Why a Product of Cyclic Groups with Non-Coprime Orders is not Cyclic

Is there an Euler-Maclaurin-like formula for products?

Maximum product of numbers that add up to 10?

Motivation and intuition behind the geometric product integral

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