Question

Probability that 2 random numbers can express another random number as positive integer linear combination?

score 106 · Answer 1 · 2023-04-07 17:37:45

106

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Probability that 2 random numbers can express another random number as positive integer linear combination?

Published on 07 Apr 2023 - 17:37

score 43 · Answer 2 · 2023-04-09 19:05:47

43

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Edwards' reasoning for why this contour integral representation of $\zeta (s)$ converges everywhere

Published on 09 Apr 2023 - 19:05

score 204 · Answer 3 · 2026-04-01 17:32:49

204

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$\xi(s)=\xi(1-s)$ functional equation from $\Gamma(s)\Gamma(s+1)\zeta(s)=\int_0^\infty t^{s-1}\sum_{\alpha \in \Bbb N} \Phi_{\alpha}(t)~ dt$

Published on 01 Apr 2026 - 17:32

score 53 · Answer 4 · 2023-04-11 00:48:13

53

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Basel problem approximation error to specific sum

Published on 11 Apr 2023 - 0:48

score 183 · Answer 5 · 2023-04-14 02:22:35

183

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Show that $ \int_1^{\infty} \frac{\operatorname{li}(x)^2 (x - 1)}{x^4} dx = \frac{5 \pi^2}{36} $

Published on 14 Apr 2023 - 2:22

score 120 · Answer 6 · 2026-03-26 03:00:39

120

Views

Critical strip...critical cuboid?

Published on 26 Mar 2026 - 3:00

score 68 · Answer 7 · 2023-04-19 12:45:03

68

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The inverse mellin transform of the reciprocal of the Archimedean factor of the Zeta function

Published on 19 Apr 2023 - 12:45

score 204 · Answer 8 · 2023-04-22 14:54:50

204

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Concerning this curious sum: $\sum_{n=1}^{\infty}\frac{2n+1}{2^{2n}}\left[\frac{n-1}{2^{2n}}-(n-2)\right]\zeta(2n+1)=\ln2$

Published on 22 Apr 2023 - 14:54

score 74 · Answer 9 · 2026-03-26 02:54:07

74

Views

Two curious related sums on $\gamma$ and $\ln2$

Published on 26 Mar 2026 - 2:54

score 79 · Answer 10 · 2026-03-25 07:45:43

79

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Different way of proving: $\sum_{n=1}^{\infty}\frac{\left(16(-1)^n+5\right)\left(\phi H_n+\frac{1}{n^3}\right)+\frac{11}{n^3}}{n^2}=\zeta(5)$

Published on 25 Mar 2026 - 7:45

score 117 · Answer 11 · 2026-03-26 16:10:15

117

Views

New asymptotic expression of $\zeta^{(m)}(1-s)$ involving generalized Stirling numbers of the $1$st kind

Published on 26 Mar 2026 - 16:10

score 109 · Answer 12 · 2023-05-02 15:53:40

109

Views

$\mathrm{Zi}_n(x)$ limits to $\pi(x).$ But exactly?

Published on 02 May 2023 - 15:53

score 208 · Answer 13 · 2023-05-05 10:10:31

208

Views

Showing $\displaystyle{\zeta(3)=\frac{1}{7}\sum_{n=1}^\infty\frac{n(2n+1)\zeta(2n+1)}{2^{2n-2}}}$

Published on 05 May 2023 - 10:10

score 237 · Answer 14 · 2026-02-23 03:03:13

237

Views

Generalized formula for the polylogarithm

Published on 23 Feb 2026 - 3:03

score 288 · Answer 15 · 2026-03-28 22:28:29

288

Views

Closed form of $\sum _{n=2}^{\infty }\zeta (n)^2 z^n$

Published on 28 Mar 2026 - 22:28

List Question

Probability that 2 random numbers can express another random number as positive integer linear combination?

Edwards' reasoning for why this contour integral representation of $\zeta (s)$ converges everywhere

$\xi(s)=\xi(1-s)$ functional equation from $\Gamma(s)\Gamma(s+1)\zeta(s)=\int_0^\infty t^{s-1}\sum_{\alpha \in \Bbb N} \Phi_{\alpha}(t)~ dt$

Basel problem approximation error to specific sum

Show that $ \int_1^{\infty} \frac{\operatorname{li}(x)^2 (x - 1)}{x^4} dx = \frac{5 \pi^2}{36} $

Critical strip...critical cuboid?

The inverse mellin transform of the reciprocal of the Archimedean factor of the Zeta function

Concerning this curious sum: $\sum_{n=1}^{\infty}\frac{2n+1}{2^{2n}}\left[\frac{n-1}{2^{2n}}-(n-2)\right]\zeta(2n+1)=\ln2$

Two curious related sums on $\gamma$ and $\ln2$

Different way of proving: $\sum_{n=1}^{\infty}\frac{\left(16(-1)^n+5\right)\left(\phi H_n+\frac{1}{n^3}\right)+\frac{11}{n^3}}{n^2}=\zeta(5)$

New asymptotic expression of $\zeta^{(m)}(1-s)$ involving generalized Stirling numbers of the $1$st kind

$\mathrm{Zi}_n(x)$ limits to $\pi(x).$ But exactly?

Showing $\displaystyle{\zeta(3)=\frac{1}{7}\sum_{n=1}^\infty\frac{n(2n+1)\zeta(2n+1)}{2^{2n-2}}}$

Generalized formula for the polylogarithm

Closed form of $\sum _{n=2}^{\infty }\zeta (n)^2 z^n$

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