Question

Expression for $\sum_{k=2}^{\infty} \frac{\zeta(k)(-1)^{2k-1}}{k!} x^{k}$?

score 72 · Answer 1 · 2021-07-07 10:20:19

72

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Expression for $\sum_{k=2}^{\infty} \frac{\zeta(k)(-1)^{2k-1}}{k!} x^{k}$?

Published on 07 Jul 2021 - 10:20

score 147 · Answer 2 · 2021-07-08 22:52:13

147

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Identity of the harmonic series

Published on 08 Jul 2021 - 22:52

score 193 · Answer 3 · 2026-03-25 16:01:10

193

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Dirichlet transform of $e^{(2 \pi i / 3) \Omega(n)}$

Published on 25 Mar 2026 - 16:01

score 57 · Answer 4 · 2021-07-12 15:01:42

57

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A sum over similar to Riemann zeta function in two dimension

Published on 12 Jul 2021 - 15:01

score 131 · Answer 5 · 2026-03-26 17:38:21

131

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What is the asymptotics of: $\Re\left(\frac{\zeta \left(1+\frac{1}{c}\right) \zeta (s+i t)}{\zeta \left(s+i t+\frac{1}{c}+1-1\right)}\right)$?

Published on 26 Mar 2026 - 17:38

score 565 · Answer 6 · 2021-07-16 00:00:30

565

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Proof verification: $\lim\limits_{s\to\infty}\zeta(s)=1$

Published on 16 Jul 2021 - 0:00

score 170 · Answer 7 · 2026-03-27 19:10:18

170

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On the integral $\int\limits_{0}^{\infty}x^{s-1}\left(\frac{e^{(1-a)x}}{e^{x}-1}-\frac{1}{x}\right)\,dx$

Published on 27 Mar 2026 - 19:10

score 100 · Answer 8 · 2026-03-26 01:35:04

100

Views

Controlling High Moments with Short Low Moments

Published on 26 Mar 2026 - 1:35

score 53 · Answer 9 · 2026-04-10 17:35:52

53

Views

Proof of identity in Montgomery and Vaughan

Published on 10 Apr 2026 - 17:35

score 106 · Answer 10 · 2026-04-10 23:53:09

106

Views

Proof in Montgomery and Vaughan

Published on 10 Apr 2026 - 23:53

score 130 · Answer 11 · 2026-04-12 19:57:19

130

Views

How to derive this series for $\gamma$ that is only involving odd integer values of $\zeta(s)$?

Published on 12 Apr 2026 - 19:57

score 274 · Answer 12 · 2021-07-20 18:28:10

274

Views

Is it possible to prove $ \lim_{ x \to \infty}M(x)/\sqrt{x} - \sum_{n \le x}\mu(n)/\sqrt{n} $ converges?

Published on 20 Jul 2021 - 18:28

score 92 · Answer 13 · 2026-04-12 19:03:15

92

Views

Is this identity related to the sum ln(n)/n^s (etc.) interesting at all?

Published on 12 Apr 2026 - 19:03

score 211 · Answer 14 · 2026-03-26 09:51:24

211

Views

Confused about the derivation of the identity: $\ln(\zeta(s))=s\int_{0} ^ {\infty} J(x)x^{-s-1}dx$ and it's relationship to Stieltjes integrals

Published on 26 Mar 2026 - 9:51

score 337 · Answer 15 · 2026-04-03 12:44:58

337

Views

Prove:$\int_{0}^{\infty} x^9K_0(x)^4\text{d}x =\frac{42777\zeta(3)-51110}{2048}$

Published on 03 Apr 2026 - 12:44

List Question

Expression for $\sum_{k=2}^{\infty} \frac{\zeta(k)(-1)^{2k-1}}{k!} x^{k}$?

Identity of the harmonic series

Dirichlet transform of $e^{(2 \pi i / 3) \Omega(n)}$

A sum over similar to Riemann zeta function in two dimension

What is the asymptotics of: $\Re\left(\frac{\zeta \left(1+\frac{1}{c}\right) \zeta (s+i t)}{\zeta \left(s+i t+\frac{1}{c}+1-1\right)}\right)$?

Proof verification: $\lim\limits_{s\to\infty}\zeta(s)=1$

On the integral $\int\limits_{0}^{\infty}x^{s-1}\left(\frac{e^{(1-a)x}}{e^{x}-1}-\frac{1}{x}\right)\,dx$

Controlling High Moments with Short Low Moments

Proof of identity in Montgomery and Vaughan

Proof in Montgomery and Vaughan

How to derive this series for $\gamma$ that is only involving odd integer values of $\zeta(s)$?

Is it possible to prove $ \lim_{ x \to \infty}M(x)/\sqrt{x} - \sum_{n \le x}\mu(n)/\sqrt{n} $ converges?

Is this identity related to the sum ln(n)/n^s (etc.) interesting at all?

Confused about the derivation of the identity: $\ln(\zeta(s))=s\int_{0} ^ {\infty} J(x)x^{-s-1}dx$ and it's relationship to Stieltjes integrals

Prove:$\int_{0}^{\infty} x^9K_0(x)^4\text{d}x =\frac{42777\zeta(3)-51110}{2048}$

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