Question

Does an integral expression exist for $\xi(s)\,\xi(-s)$?

score 113 · Answer 1 · 2026-04-09 10:48:21

113

Views

Does an integral expression exist for $\xi(s)\,\xi(-s)$?

Published on 09 Apr 2026 - 10:48

score 145 · Answer 2 · 2026-03-27 05:41:48

145

Views

Proving the "identity" $\frac{\zeta^{2}(s)}{\zeta(2 s) J(s)}=\frac{\zeta^{2}(-s)}{\zeta(-2 s) J(-s)}$

Published on 27 Mar 2026 - 5:41

score 91 · Answer 3 · 2020-08-31 10:58:30

91

Views

Riemann Prime numbers less than a given quantity

Published on 31 Aug 2020 - 10:58

score 50 · Answer 4 · 2026-04-09 17:56:58

50

Views

Could this 'split up' integral expression for $\xi(s)$ be simplified further?

Published on 09 Apr 2026 - 17:56

score 45 · Answer 5 · 2026-04-10 06:09:27

45

Views

A question about function related to Riemann zeta function

Published on 10 Apr 2026 - 6:09

score 88 · Answer 6 · 2026-03-26 22:58:21

88

Views

Calculate $\int_1^\infty \frac{ (1-x+[x])(x^{1-\sigma}-x^\sigma)cos(ln x)}{x^2}dx$

Published on 26 Mar 2026 - 22:58

score 1.5k · Answer 7 · 2020-09-09 07:50:52

1.5k

Views

Prove $\int_0^{\infty }\frac1{\sqrt{x}}\left(\frac{\cos(\pi x^2)}{\sinh (\pi x)}-\frac1{\pi x}\right)dx=\frac{1}{\sqrt{2}}\zeta(\frac{1}{2})$

Published on 09 Sep 2020 - 7:50

score 80 · Answer 8 · 2026-03-27 05:38:59

80

Views

Understanding the functional equation $\left( \frac{2}{\pi} \right)^s \sin \left( \frac{\pi s}{2} \right) \Gamma(s)L(s)= L(1-s).$

Published on 27 Mar 2026 - 5:38

score 110 · Answer 9 · 2026-04-10 17:58:50

110

Views

Are there variations of Ramaswami's formula for the analytic continuation of the Riemann zeta function?

Published on 10 Apr 2026 - 17:58

score 267 · Answer 10 · 2026-04-02 19:35:35

267

Views

Improving an approximation for the inverse of the Riemann–Siegel θ-function

Published on 02 Apr 2026 - 19:35

score 43 · Answer 11 · 2026-04-10 19:54:35

43

Views

Prove that following integral function has only real zeros.

Published on 10 Apr 2026 - 19:54

score 208 · Answer 12 · 2020-09-18 13:13:01

208

Views

Some questions on the identity $\sum_{n=k+2}^{\infty} \binom{n-1}{k} (\zeta(n) -1) = 1 $

Published on 18 Sep 2020 - 13:13

score 53 · Answer 13 · 2026-03-26 22:50:14

53

Views

Bounding summation

Published on 26 Mar 2026 - 22:50

score 293 · Answer 14 · 2020-09-25 02:09:52

293

Views

How to solve $\int\limits_0^x {x^n \over{1 + e^x}} dx$?

Published on 25 Sep 2020 - 2:09

score 133 · Answer 15 · 2026-04-03 05:48:17

133

Views

Show the integral : $\int_{0}^{\infty}\ln^2\Big(e^{-x}+1\Big)dx=\frac{\zeta(3)}{4}$

Published on 03 Apr 2026 - 5:48

List Question

Does an integral expression exist for $\xi(s)\,\xi(-s)$?

Proving the "identity" $\frac{\zeta^{2}(s)}{\zeta(2 s) J(s)}=\frac{\zeta^{2}(-s)}{\zeta(-2 s) J(-s)}$

Riemann Prime numbers less than a given quantity

Could this 'split up' integral expression for $\xi(s)$ be simplified further?

A question about function related to Riemann zeta function

Calculate $\int_1^\infty \frac{ (1-x+[x])(x^{1-\sigma}-x^\sigma)cos(ln x)}{x^2}dx$

Prove $\int_0^{\infty }\frac1{\sqrt{x}}\left(\frac{\cos(\pi x^2)}{\sinh (\pi x)}-\frac1{\pi x}\right)dx=\frac{1}{\sqrt{2}}\zeta(\frac{1}{2})$

Understanding the functional equation $\left( \frac{2}{\pi} \right)^s \sin \left( \frac{\pi s}{2} \right) \Gamma(s)L(s)= L(1-s).$

Are there variations of Ramaswami's formula for the analytic continuation of the Riemann zeta function?

Improving an approximation for the inverse of the Riemann–Siegel θ-function

Prove that following integral function has only real zeros.

Some questions on the identity $\sum_{n=k+2}^{\infty} \binom{n-1}{k} (\zeta(n) -1) = 1 $

Bounding summation

How to solve $\int\limits_0^x {x^n \over{1 + e^x}} dx$?

Show the integral : $\int_{0}^{\infty}\ln^2\Big(e^{-x}+1\Big)dx=\frac{\zeta(3)}{4}$

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