Question

Are there any real analytic functions such that $\sum_{n=1}^{\infty} \frac{1}{f(n)} = \sum_{k=2}^{\infty} f(k) \left( \zeta(k) - 1 \right) $?

score 110 · Answer 1 · 2026-04-02 08:19:38

110

Views

Are there any real analytic functions such that $\sum_{n=1}^{\infty} \frac{1}{f(n)} = \sum_{k=2}^{\infty} f(k) \left( \zeta(k) - 1 \right) $?

Published on 02 Apr 2026 - 8:19

score 89 · Answer 2 · 2026-03-30 07:28:22

89

Views

Series involving $\sum_{m,n}\frac{1}{(m^2+n^2)^{2k}}$

Published on 30 Mar 2026 - 7:28

score 70 · Answer 3 · 2023-10-27 18:19:14

70

Views

Does this series representation for $\zeta(s)$ converge in the critical strip?

Published on 27 Oct 2023 - 18:19

score 131 · Answer 4 · 2026-02-23 04:50:07

131

Views

The ultimate polylogarithm ladder

Published on 23 Feb 2026 - 4:50

score 66 · Answer 5 · 2023-10-29 14:24:45

66

Views

Evaluate $\zeta(2)$ by limit

Published on 29 Oct 2023 - 14:24

score 60 · Answer 6 · 2026-03-27 04:18:41

60

Views

Integrability of the Jacobi Theta Function

Published on 27 Mar 2026 - 4:18

score 264 · Answer 7 · 2026-03-26 06:31:55

264

Views

Using Ramanujan-type series for $1/\pi^m$ to find formulas for $\zeta(2),\, \zeta(3),\, \zeta(4)$?

Published on 26 Mar 2026 - 6:31

score 72 · Answer 8 · 2023-11-03 03:10:26

72

Views

What does the zeta squared function converge to

Published on 03 Nov 2023 - 3:10

score 277 · Answer 9 · 2026-03-26 06:08:10

277

Views

Explore the relationship between $\sum\limits_{n = 1}^{2x} \frac{1}{{n^s}^x}$ and $\sum\limits_{n = 1}^{2x-1} \frac{(-1)^{n-1}}{{n^s}^x}$

Published on 26 Mar 2026 - 6:08

score 84 · Answer 10 · 2026-03-30 07:20:42

84

Views

Relationships between Riemann Xi and Jacobi Theta functions

Published on 30 Mar 2026 - 7:20

score 79 · Answer 11 · 2026-04-02 02:40:31

79

Views

Using Riemann's methods to derive the floor function of x from the zeta function

Published on 02 Apr 2026 - 2:40

score 68 · Answer 12 · 2023-11-06 04:22:09

68

Views

Applying Euler's trick for the Basel problem to cos leads to a wrong result?

Published on 06 Nov 2023 - 4:22

score 47 · Answer 13 · 2026-03-26 17:35:34

47

Views

Riemann zeta conjugate extension to real plane < 1

Published on 26 Mar 2026 - 17:35

score 105 · Answer 14 · 2023-11-07 01:35:19

105

Views

Asymptotic Behavior of Riemann Zeta Function

Published on 07 Nov 2023 - 1:35

score 80 · Answer 15 · 2026-03-25 17:37:20

80

Views

Functional equation for $\theta$ function using functional equation of $\zeta(s)$

Published on 25 Mar 2026 - 17:37

List Question

Are there any real analytic functions such that $\sum_{n=1}^{\infty} \frac{1}{f(n)} = \sum_{k=2}^{\infty} f(k) \left( \zeta(k) - 1 \right) $?

Series involving $\sum_{m,n}\frac{1}{(m^2+n^2)^{2k}}$

Does this series representation for $\zeta(s)$ converge in the critical strip?

The ultimate polylogarithm ladder

Evaluate $\zeta(2)$ by limit

Integrability of the Jacobi Theta Function

Using Ramanujan-type series for $1/\pi^m$ to find formulas for $\zeta(2),\, \zeta(3),\, \zeta(4)$?

What does the zeta squared function converge to

Explore the relationship between $\sum\limits_{n = 1}^{2x} \frac{1}{{n^s}^x}$ and $\sum\limits_{n = 1}^{2x-1} \frac{(-1)^{n-1}}{{n^s}^x}$

Relationships between Riemann Xi and Jacobi Theta functions

Using Riemann's methods to derive the floor function of x from the zeta function

Applying Euler's trick for the Basel problem to cos leads to a wrong result?

Riemann zeta conjugate extension to real plane < 1

Asymptotic Behavior of Riemann Zeta Function

Functional equation for $\theta$ function using functional equation of $\zeta(s)$

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