List questions from bernoulli-polynomials

Published on 20 Jan 2020 - 2:08

48

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Does $\sum_{n=0}^{\infty}\frac{B_{n-1}}{n!}B_n(z)$ have closed form?

Published on 09 Feb 2020 - 18:19

60

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Verifying Big O of remainder term when deriving Stirling's approximation formula

Published on 19 Feb 2020 - 10:29

120

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Are the Bernoulli numbers $B_{2n}$ given by an elementary function of $n$?

Published on 06 Jun 2020 - 3:18

332

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Sum $\sum_{(k_1, k_2, k_3): k_1+k_2+k_3=K, \,\, n_1+n_2+n_3=N}k_1^{n_1}\times k_2^{n_2} \times k_3^{n_3}$

Published on 19 Jul 2020 - 15:51

340

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Generalization of the Bernoulli polynomials ( in relation to the Index )

Published on 01 Sep 2016 - 20:41

2.3k

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The sum of fractional powers $\sum\limits_{k=1}^x k^t$.

Published on 02 Sep 2016 - 14:43

67

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Bernoulli Differential Equations

Published on 19 Nov 2016 - 16:15

129

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Is there any answer for this Bernoulli difference?

Published on 22 Nov 2016 - 11:11

207

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

Published on 29 Jan 2017 - 18:38

122

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Misunderstanding about Bernoulli-Euler relation?

Published on 18 Mar 2017 - 21:47

42

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Approximation of the Bernoulli periodic function

Published on 29 Jan 2023 - 17:37

84

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Integral expression involving Bernoulli polynomial that allows to sum a trigonometric integral series.

Published on 24 Apr 2023 - 9:54

76

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How to derive this polylogarithm identity (involving Bernoulli polynomials)?

Published on 17 May 2023 - 3:49

143

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Proving that $\lim_{ n \to \infty} \left\{ \frac{1}{2^{m n}} \sum_{r=1}^{2^n-1}(-1)^r r^m\right\}=-\frac{1}{2}$ independently of the value of $m$.

Published on 11 Sep 2023 - 19:12

List Question

Probabilities with ${ n \choose k}$

Does $\sum_{n=0}^{\infty}\frac{B_{n-1}}{n!}B_n(z)$ have closed form?

Verifying Big O of remainder term when deriving Stirling's approximation formula

Are the Bernoulli numbers $B_{2n}$ given by an elementary function of $n$?

Sum $\sum_{(k_1, k_2, k_3): k_1+k_2+k_3=K, \,\, n_1+n_2+n_3=N}k_1^{n_1}\times k_2^{n_2} \times k_3^{n_3}$

Generalization of the Bernoulli polynomials ( in relation to the Index )

The sum of fractional powers $\sum\limits_{k=1}^x k^t$.

Bernoulli Differential Equations

Is there any answer for this Bernoulli difference?

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

Misunderstanding about Bernoulli-Euler relation?

Approximation of the Bernoulli periodic function

Integral expression involving Bernoulli polynomial that allows to sum a trigonometric integral series.

How to derive this polylogarithm identity (involving Bernoulli polynomials)?

Proving that $\lim_{ n \to \infty} \left\{ \frac{1}{2^{m n}} \sum_{r=1}^{2^n-1}(-1)^r r^m\right\}=-\frac{1}{2}$ independently of the value of $m$.

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