Question

How to Prove : $ \gamma +\ln\left(\frac{\pi}{4}\right) = \sum_{n=2}^{\infty} \frac{(-1)^{n} \zeta{(n)}}{2^{n-1}n} $

score 160 · Answer 1 · 2026-03-25 09:28:55

160

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How to Prove : $ \gamma +\ln\left(\frac{\pi}{4}\right) = \sum_{n=2}^{\infty} \frac{(-1)^{n} \zeta{(n)}}{2^{n-1}n} $

Published on 25 Mar 2026 - 9:28

score 70 · Answer 2 · 2026-03-26 11:02:11

70

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Why is $\sum_{n=1}^\infty (-1)^n\frac{\zeta(2n)}{\pi^{2n}} = \frac{1}{1-e^2}$?

Published on 26 Mar 2026 - 11:02

score 93 · Answer 3 · 2020-06-16 05:45:13

93

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Is $\int_0^1\int_0^1 \frac{Li_3(xy)}{(xy)^2}dxdy$ equal to $3\zeta(2)+\zeta(3)-6$ or to infinity?

Published on 16 Jun 2020 - 5:45

score 148 · Answer 4 · 2026-03-26 04:30:46

148

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Variation of the Riemann Zeta Function

Published on 26 Mar 2026 - 4:30

score 56 · Answer 5 · 2026-03-30 15:27:14

56

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Calculating the residue of given quantity

Published on 30 Mar 2026 - 15:27

score 122 · Answer 6 · 2026-03-26 13:00:54

122

Views

Series of square of factorial

Published on 26 Mar 2026 - 13:00

score 38 · Answer 7 · 2020-06-23 14:08:53

38

Views

Show that $f(s)=\sum \frac{1}{n^s}$ is continuous for $Re(s)>1$

Published on 23 Jun 2020 - 14:08

score 248 · Answer 8 · 2020-06-23 19:26:04

248

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Show that $\sum_{j=1}^{\infty}\dfrac{\zeta(6j-3)-1}{2j-1} =\frac12\ln(3/2) $

Published on 23 Jun 2020 - 19:26

score 380 · Answer 9 · 2026-03-29 07:00:40

380

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Is there any closed form for $\displaystyle \prod_{n=1}^{\infty} \left(1-\frac{1}{\zeta(n)}\right)$

Published on 29 Mar 2026 - 7:00

score 81 · Answer 10 · 2026-03-29 07:00:28

Are there any values of $m$ other than $3$ such that $\prod_{k=2}^{\infty}\dfrac{(k^m-1)}{ (k^m+1)} $ has some kind of known form?

score 108 · Answer 11 · 2026-03-30 17:08:13

108

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Residues of the (modern) Approximate Functional Equation

Published on 30 Mar 2026 - 17:08

score 79 · Answer 12 · 2020-06-26 17:15:13

79

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Sum $\sum\limits_{n=0}^{\infty}(-1)^{n-1}\frac1{(2n+1)^3}$

Published on 26 Jun 2020 - 17:15

score 181 · Answer 13 · 2020-06-28 17:59:27

181

Views

Different ways of evaluating $\int_{0}^{\infty}\frac{x^n dx}{(e^x-1)^2}$

Published on 28 Jun 2020 - 17:59

score 58 · Answer 14 · 2020-07-02 16:49:17

58

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Speed of decay of $\zeta(x)-1$ as $x \to \infty$

Published on 02 Jul 2020 - 16:49

score 152 · Answer 15 · 2020-07-06 05:14:04

152

Views

Are the $\Im(s)$ for zeros of the Riemann zeta function isolated values?

Published on 06 Jul 2020 - 5:14

List Question

How to Prove : $ \gamma +\ln\left(\frac{\pi}{4}\right) = \sum_{n=2}^{\infty} \frac{(-1)^{n} \zeta{(n)}}{2^{n-1}n} $

Why is $\sum_{n=1}^\infty (-1)^n\frac{\zeta(2n)}{\pi^{2n}} = \frac{1}{1-e^2}$?

Is $\int_0^1\int_0^1 \frac{Li_3(xy)}{(xy)^2}dxdy$ equal to $3\zeta(2)+\zeta(3)-6$ or to infinity?

Variation of the Riemann Zeta Function

Calculating the residue of given quantity

Series of square of factorial

Show that $f(s)=\sum \frac{1}{n^s}$ is continuous for $Re(s)>1$

Show that $\sum_{j=1}^{\infty}\dfrac{\zeta(6j-3)-1}{2j-1} =\frac12\ln(3/2) $

Is there any closed form for $\displaystyle \prod_{n=1}^{\infty} \left(1-\frac{1}{\zeta(n)}\right)$

Are there any values of $m$ other than $3$ such that $\prod_{k=2}^{\infty}\dfrac{(k^m-1)}{ (k^m+1)} $ has some kind of known form?

Residues of the (modern) Approximate Functional Equation

Sum $\sum\limits_{n=0}^{\infty}(-1)^{n-1}\frac1{(2n+1)^3}$

Different ways of evaluating $\int_{0}^{\infty}\frac{x^n dx}{(e^x-1)^2}$

Speed of decay of $\zeta(x)-1$ as $x \to \infty$

Are the $\Im(s)$ for zeros of the Riemann zeta function isolated values?

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