List questions from bernoulli-numbers

Published on 11 Apr 2021 - 7:53

197

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Getting $B_4$ from the recursive definition $B_n=1-\sum_{k=0}^{n-1}{n\choose k}\frac{B_k}{n-k+1}$

Published on 25 Apr 2021 - 18:34

210

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Conjecture on bernoulli numbers and binomial coefficients

Published on 25 Apr 2021 - 23:13

157

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Correlation between union of correlated Bernoulli processes

Published on 27 Apr 2021 - 13:56

696

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how to prove that $1^x+2^x+3^x+4^x+\cdots+N^x$ will never sum to a prime number except $1^x+2^x$?

Published on 01 May 2021 - 1:00

54

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Merged Poisson Process Rate

Published on 03 May 2021 - 3:47

111

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What's the nicest proof of the formula for the sum of the $k$-th powers of the first natural numbers?

Published on 23 Feb 2026 - 6:41

130

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Dirichlet series of Bernoulli polynomials

Published on 23 Feb 2026 - 6:36

70

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Residue of $\dfrac{\mathrm{e}^\frac{2}{z}}{\sin z}$ at $0$

Published on 16 May 2021 - 14:08

99

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Two properties of the set of Bernoulli numbers

Published on 27 Mar 2026 - 0:05

179

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Evaluating $\int_0^y \frac{z^2e^{az}}{e^z-1}\,\mathrm dz$.

Published on 16 Jun 2021 - 14:56

131

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Is the determinant of a Hessenberg matrix whose elements are the Bernoulli numbers positive?

Published on 30 Jun 2021 - 15:03

170

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Sum a product of Bernoulli numbers and binomial coefficients

Published on 26 Mar 2026 - 6:05

64

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A polynomial rep. for $\frac{1}{m!} \sum_{k=0}^n (-1)^{k+m} \frac{k^n}{k+1} \binom{m}{k}$

Published on 14 Jul 2021 - 18:01

86

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Bernoulli Polynomials and Euler summation

Published on 23 Feb 2026 - 6:34

List Question

Finding an integral using Bernoulli Numbers exponential generating function

Getting $B_4$ from the recursive definition $B_n=1-\sum_{k=0}^{n-1}{n\choose k}\frac{B_k}{n-k+1}$

Conjecture on bernoulli numbers and binomial coefficients

Correlation between union of correlated Bernoulli processes

how to prove that $1^x+2^x+3^x+4^x+\cdots+N^x$ will never sum to a prime number except $1^x+2^x$?

Merged Poisson Process Rate

What's the nicest proof of the formula for the sum of the $k$-th powers of the first natural numbers?

Dirichlet series of Bernoulli polynomials

Residue of $\dfrac{\mathrm{e}^\frac{2}{z}}{\sin z}$ at $0$

Two properties of the set of Bernoulli numbers

Evaluating $\int_0^y \frac{z^2e^{az}}{e^z-1}\,\mathrm dz$.

Is the determinant of a Hessenberg matrix whose elements are the Bernoulli numbers positive?

Sum a product of Bernoulli numbers and binomial coefficients

A polynomial rep. for $\frac{1}{m!} \sum_{k=0}^n (-1)^{k+m} \frac{k^n}{k+1} \binom{m}{k}$

Bernoulli Polynomials and Euler summation

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