List questions from bernoulli-numbers

Published on 12 Dec 2014 - 10:49

243

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Proper Bernoulli Function Generating Function

Published on 12 Dec 2014 - 14:51

82

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If $\chi$ is even, why is $B_{n,\chi\omega^{-n}}$ nonzero?

Published on 25 Mar 2026 - 6:28

159

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how to calculate the cumulative distribution function of sums of n Bernoulli distribution?

Published on 18 Oct 2019 - 3:12

105

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How to associate Bernouli numbers or Bernouli polynomials into the relation $ \sum_{n=0}^{\infty} \left[n(4x-1)+(2x) \right]x^n=0$?

Published on 23 Feb 2026 - 1:23

123

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Please explain how we get the equation $\sum_{n=0}^{\infty} n![(n+1)B_{n+1}-B_n]=-1$

Published on 23 Oct 2019 - 13:39

165

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how the following formula or any other explicit formula for computing Bernoulli numbers can be derived?

Published on 30 Oct 2019 - 9:35

221

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Series expansion for $f(x)=\frac{x}{e^x-1}$

Published on 03 Nov 2019 - 20:47

31

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If a $\epsilon$ ℤ, show $a(a^m-1)B_m$ $\epsilon$ ℤ for all $m>0$

Published on 12 Nov 2019 - 5:26

96

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How do you prove the following inequality according to Chernoff's bound?

Published on 16 Nov 2019 - 7:48

99

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Estimate $\sum_{n = 0}^N \cos (\alpha n^2)$

Published on 17 Nov 2019 - 6:17

603

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Bernoulli numbers tend to infinity

Published on 26 Nov 2019 - 13:10

563

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Probability of k heads being the longest run in a row in n flips?

Published on 29 Nov 2019 - 18:46

36

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Explicit $ f_k (n) $ as a function of $ k, n $

Published on 05 Dec 2019 - 15:23

41

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multiple sums when lower bound depends on previous index

Published on 24 Mar 2026 - 21:42

List Question

Bernoulli Trials with dependent events

Proper Bernoulli Function Generating Function

If $\chi$ is even, why is $B_{n,\chi\omega^{-n}}$ nonzero?

how to calculate the cumulative distribution function of sums of n Bernoulli distribution?

How to associate Bernouli numbers or Bernouli polynomials into the relation $ \sum_{n=0}^{\infty} \left[n(4x-1)+(2x) \right]x^n=0$?

Please explain how we get the equation $\sum_{n=0}^{\infty} n![(n+1)B_{n+1}-B_n]=-1$

how the following formula or any other explicit formula for computing Bernoulli numbers can be derived?

Series expansion for $f(x)=\frac{x}{e^x-1}$

If a $\epsilon$ ℤ, show $a(a^m-1)B_m$ $\epsilon$ ℤ for all $m>0$

How do you prove the following inequality according to Chernoff's bound?

Estimate $\sum_{n = 0}^N \cos (\alpha n^2)$

Bernoulli numbers tend to infinity

Probability of k heads being the longest run in a row in n flips?

Explicit $ f_k (n) $ as a function of $ k, n $

multiple sums when lower bound depends on previous index

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