Question

On the integral representation of the function $b(s)$ defining $b(n)=\operatorname{Bernoulli}_{2n}$, and Riemann's trick

score 33 · Answer 1 · 2016-12-07 19:54:52

33

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On the integral representation of the function $b(s)$ defining $b(n)=\operatorname{Bernoulli}_{2n}$, and Riemann's trick

Published on 07 Dec 2016 - 19:54

score 287 · Answer 2 · 2016-12-24 04:15:34

287

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Why are the Bernoulli numbers of even index nonzero?

Published on 24 Dec 2016 - 4:15

score 344 · Answer 3 · 2017-01-09 06:29:57

344

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Very accurate approximations for $\sum\limits_{n=0}^\infty \frac{n}{a^n-1}$ and $\sum\limits_{n=0}^\infty \frac{n^{2m+1}}{e^n-1}$

Published on 09 Jan 2017 - 6:29

score 4.9k · Answer 4 · 2017-01-15 16:11:30

4.9k

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Bernoulli numbers, taylor series expansion of tan x

Published on 15 Jan 2017 - 16:11

score 97 · Answer 5 · 2017-01-21 06:59:34

97

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Can someone help me to find the closed form of this series: $\sum_{k=1}^\infty \frac{(-1)^k B_{k+1}}{k+1}$?

Published on 21 Jan 2017 - 6:59

score 363 · Answer 6 · 2017-01-21 08:39:33

363

Views

Is the sequence of the even Bernoulli numbers bounded?

Published on 21 Jan 2017 - 8:39

score 139 · Answer 7 · 2017-01-22 13:05:13

139

Views

Absolute value of numerator of $2k$-th Bernoulli number $> 1$ for $k >4$.

Published on 22 Jan 2017 - 13:05

score 208 · Answer 8 · 2026-02-23 02:59:30

208

Views

Stirling numbers and bernoulli numbers for summing up n numbers to the kth power

Published on 23 Feb 2026 - 2:59

score 61 · Answer 9 · 2017-02-11 08:17:54

61

Views

$ \sum_{r=0}^{n}\binom{2n}{2r}(2-4^r)\beta_{2r}=2^{2n}\beta_{2n}$ - sum involving bernoulli numbers

Published on 11 Feb 2017 - 8:17

score 1.3k · Answer 10 · 2017-02-13 19:08:39

1.3k

Views

Variance in a Bernoulli distribution.

Published on 13 Feb 2017 - 19:08

score 257 · Answer 11 · 2017-02-14 23:36:41

257

Views

Finding the Corresponding Polynomial

Published on 14 Feb 2017 - 23:36

score 10.4k · Answer 12 · 2017-02-27 07:01:48

10.4k

Views

Solve the Bernoulli differential equation.

Published on 27 Feb 2017 - 7:01

score 71 · Answer 13 · 2017-02-27 17:59:11

71

Views

How to prove this Bernoulli summation

Published on 27 Feb 2017 - 17:59

score 366 · Answer 14 · 2017-03-10 01:33:21

366

Views

Faulhaber's Formula proof

Published on 10 Mar 2017 - 1:33

score 127 · Answer 15 · 2017-03-12 21:37:01

127

Views

Summation of divergent series $1-2^p+3^p-4^p+\ldots$

Published on 12 Mar 2017 - 21:37

List Question

On the integral representation of the function $b(s)$ defining $b(n)=\operatorname{Bernoulli}_{2n}$, and Riemann's trick

Why are the Bernoulli numbers of even index nonzero?

Very accurate approximations for $\sum\limits_{n=0}^\infty \frac{n}{a^n-1}$ and $\sum\limits_{n=0}^\infty \frac{n^{2m+1}}{e^n-1}$

Bernoulli numbers, taylor series expansion of tan x

Can someone help me to find the closed form of this series: $\sum_{k=1}^\infty \frac{(-1)^k B_{k+1}}{k+1}$?

Is the sequence of the even Bernoulli numbers bounded?

Absolute value of numerator of $2k$-th Bernoulli number $> 1$ for $k >4$.

Stirling numbers and bernoulli numbers for summing up n numbers to the kth power

$ \sum_{r=0}^{n}\binom{2n}{2r}(2-4^r)\beta_{2r}=2^{2n}\beta_{2n}$ - sum involving bernoulli numbers

Variance in a Bernoulli distribution.

Finding the Corresponding Polynomial

Solve the Bernoulli differential equation.

How to prove this Bernoulli summation

Faulhaber's Formula proof

Summation of divergent series $1-2^p+3^p-4^p+\ldots$

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