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On $\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\eta'(s)\frac{x^s}{s\zeta(s)}ds$, for $c>1$, where $\eta(s)$ is the Dirichlet Eta function

score 67 · Answer 1 · 2026-04-16 00:16:32

67

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On $\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\eta'(s)\frac{x^s}{s\zeta(s)}ds$, for $c>1$, where $\eta(s)$ is the Dirichlet Eta function

Published on 16 Apr 2026 - 0:16

score 107 · Answer 2 · 2026-05-10 19:40:43

107

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Questions on Convergence of $\int_1^\infty\left(\psi(x)-x\right)\ x^{-s-1}\ dx$ and $\int_1^\infty\left(\psi'(x)-1\right)\ x^{-s}\ dx$

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score 141 · Answer 3 · 2026-04-12 08:41:15

141

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score 363 · Answer 4 · 2026-04-27 22:43:40

363

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score 106 · Answer 5 · 2026-03-25 15:37:45

106

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score 151 · Answer 6 · 2026-03-25 15:41:00

151

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score 59 · Answer 7 · 2026-03-25 15:47:20

59

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score 51 · Answer 8 · 2026-03-25 15:37:52

51

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score 72 · Answer 9 · 2026-03-25 15:41:05

72

Views

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score 148 · Answer 10 · 2026-03-25 15:41:22

148

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score 81 · Answer 11 · 2026-03-25 15:41:14

81

Views

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score 44 · Answer 12 · 2026-03-25 15:42:25

44

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Evaluate $\lim_{s \rightarrow 1^{-}} \frac{\Gamma(b-as)}{\Gamma(s)\Gamma(1-s)}$, for $a,b>0$

Published on 25 Mar 2026 - 15:42

score 115 · Answer 13 · 2026-03-25 15:42:38

115

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Why does an additional -1/x term in the integrand of the Mellin transform representation of the Riemann zeta function not change its value?

Published on 25 Mar 2026 - 15:42

score 46 · Answer 14 · 2026-03-25 15:38:55

46

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score 52 · Answer 15 · 2026-04-13 20:24:08

52

Views

What's the pdf of the product of one continuous random variable and a discrete one?

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List Question

On $\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\eta'(s)\frac{x^s}{s\zeta(s)}ds$, for $c>1$, where $\eta(s)$ is the Dirichlet Eta function

Questions on Convergence of $\int_1^\infty\left(\psi(x)-x\right)\ x^{-s-1}\ dx$ and $\int_1^\infty\left(\psi'(x)-1\right)\ x^{-s}\ dx$

what is the name of this formula ? with mellin transform

Derivation of an integral containing the complete elliptic integral of the first kind

Different methods for solving a linear first order partial differential equation

Transporting orbit space of vector field via integral transform

Growth rate of Mellin transform

Another Mellin transform question

Mellin transform of sin(x) .

How to solve $\int_{-1}^{\infty}\frac{dx}{\sqrt{x^3+1}}$

Verification of integral representation of zeta function

Evaluate $\lim_{s \rightarrow 1^{-}} \frac{\Gamma(b-as)}{\Gamma(s)\Gamma(1-s)}$, for $a,b>0$

Why does an additional -1/x term in the integrand of the Mellin transform representation of the Riemann zeta function not change its value?

Preforming an explicit inverse Mellin transform

What's the pdf of the product of one continuous random variable and a discrete one?

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