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

score 64 · Answer 1 · 2017-03-18 10:48:30

64

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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 18 Mar 2017 - 10:48

score 104 · Answer 2 · 2026-03-25 07:45:53

104

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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 138 · Answer 3 · 2017-04-06 17:16:31

138

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score 361 · Answer 4 · 2026-02-23 15:09:43

361

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score 105 · Answer 5 · 2023-02-07 08:45:09

105

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score 150 · Answer 6 · 2023-02-09 16:39:53

150

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58

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50

Views

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score 71 · Answer 9 · 2023-02-26 06:56:05

71

Views

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score 147 · Answer 10 · 2023-03-06 19:41:10

147

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score 80 · Answer 11 · 2023-03-07 02:29:41

80

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score 43 · Answer 12 · 2023-03-07 08:08:30

43

Views

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Published on 07 Mar 2023 - 8:08

score 114 · Answer 13 · 2023-03-08 14:25:06

114

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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 08 Mar 2023 - 14:25

score 45 · Answer 14 · 2023-03-21 17:10:05

45

Views

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score 49 · Answer 15 · 2023-04-19 14:02:32

49

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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