Question

Proving $\mathcal{M}\left(\sin(x)\right)(s) = \Gamma(s)\sin\left(\frac{\pi}{2}s \right)$ using Real Analysis

score 369 · Answer 1 · 2019-02-14 00:25:05

369

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Proving $\mathcal{M}\left(\sin(x)\right)(s) = \Gamma(s)\sin\left(\frac{\pi}{2}s \right)$ using Real Analysis

Published on 14 Feb 2019 - 0:25

score 227 · Answer 2 · 2019-02-16 02:24:49

227

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Question related to derived formula for zeta-zero counting function

Published on 16 Feb 2019 - 2:24

score 277 · Answer 3 · 2019-02-16 21:32:47

277

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Mellin inverse of $\sum_{n=0}^{\infty}\frac{\Gamma(n+s)\zeta(n+s)\zeta(n+1+s)}{\zeta(s)n!}\left(-\omega\right)^{n}$

Published on 16 Feb 2019 - 21:32

score 55 · Answer 4 · 2019-02-18 07:28:32

55

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Existence of classical Dirichlet series from Lebesgue integrable inverse Mellin transform

Published on 18 Feb 2019 - 7:28

score 66 · Answer 5 · 2026-03-24 23:42:41

66

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Mellin transform involving $\sinh({A_1}/2)$

Published on 24 Mar 2026 - 23:42

score 75 · Answer 6 · 2019-03-08 08:00:18

75

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Mellin Transform problem

Published on 08 Mar 2019 - 8:00

score 77 · Answer 7 · 2026-03-25 01:17:06

77

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Is $\int_0^1 \Psi(x)\Psi(1-x)\,dx$ related to any transform?

Published on 25 Mar 2026 - 1:17

score 543 · Answer 8 · 2019-03-12 18:56:44

543

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Mellin Transform $M[\log(x)f(x)] = \frac{d}{ds}F(s)$

Published on 12 Mar 2019 - 18:56

score 149 · Answer 9 · 2019-03-19 18:46:39

149

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What is the Dirichlet Transform of $a(n)=\frac{\mu(n)}{n^2}\,\log\left(\frac{2\,\pi}{n}\right)$?

Published on 19 Mar 2019 - 18:46

score 112 · Answer 10 · 2019-04-14 20:22:00

112

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Question about Dirichlet Series Related to Formula for $\frac{1}{e}$

Published on 14 Apr 2019 - 20:22

score 35 · Answer 11 · 2019-04-25 09:16:05

35

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Does the notion of Mellin transform make sense for complex functions as well?

Published on 25 Apr 2019 - 9:16

score 364 · Answer 12 · 2019-04-27 02:00:08

364

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Analytic Continuation of Mellin Transforms and the Prime Zeta Function

Published on 27 Apr 2019 - 2:00

score 72 · Answer 13 · 2019-06-13 20:20:23

72

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Residue of function with $\frac{1}{\ln(z^{-2})}$ and $z^{-2}$ dependence

Published on 13 Jun 2019 - 20:20

score 140 · Answer 14 · 2019-06-27 16:37:14

140

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Questions about the Dirichlet series $K(s)=\sum\limits_{p^k} p^{\,-k\,s}$

Published on 27 Jun 2019 - 16:37

score 367 · Answer 15 · 2019-07-03 13:04:58

367

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How Does Ramanujan’s Master Theorem Work?

Published on 03 Jul 2019 - 13:04

List Question

Proving $\mathcal{M}\left(\sin(x)\right)(s) = \Gamma(s)\sin\left(\frac{\pi}{2}s \right)$ using Real Analysis

Question related to derived formula for zeta-zero counting function

Mellin inverse of $\sum_{n=0}^{\infty}\frac{\Gamma(n+s)\zeta(n+s)\zeta(n+1+s)}{\zeta(s)n!}\left(-\omega\right)^{n}$

Existence of classical Dirichlet series from Lebesgue integrable inverse Mellin transform

Mellin transform involving $\sinh({A_1}/2)$

Mellin Transform problem

Is $\int_0^1 \Psi(x)\Psi(1-x)\,dx$ related to any transform?

Mellin Transform $M[\log(x)f(x)] = \frac{d}{ds}F(s)$

What is the Dirichlet Transform of $a(n)=\frac{\mu(n)}{n^2}\,\log\left(\frac{2\,\pi}{n}\right)$?

Question about Dirichlet Series Related to Formula for $\frac{1}{e}$

Does the notion of Mellin transform make sense for complex functions as well?

Analytic Continuation of Mellin Transforms and the Prime Zeta Function

Residue of function with $\frac{1}{\ln(z^{-2})}$ and $z^{-2}$ dependence

Questions about the Dirichlet series $K(s)=\sum\limits_{p^k} p^{\,-k\,s}$

How Does Ramanujan’s Master Theorem Work?

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