Question

What is the sum of the series $\sum_{r = 1}^{n-1}{1 \over r \sqrt[a]{\log \big(\frac{\log n}{\log r}\big)}}$?

score 125 · Answer 1 · 2023-04-04 05:41:53

125

Views

What is the sum of the series $\sum_{r = 1}^{n-1}{1 \over r \sqrt[a]{\log \big(\frac{\log n}{\log r}\big)}}$?

Published on 04 Apr 2023 - 5:41

score 128 · Answer 2 · 2026-03-28 11:54:15

128

Views

What is $\lim_{x\to \infty}f(x)=\lim_{x\to \infty}\int_{0}^{x}\prod_{n=1}^{\infty}\left(1-e^{-t-n}\right)dt-x+1$

Published on 28 Mar 2026 - 11:54

score 173 · Answer 3 · 2026-03-26 02:53:55

173

Views

How can I evaluate this infinite sum?

Published on 26 Mar 2026 - 2:53

score 100 · Answer 4 · 2023-04-06 05:36:51

100

Views

Limit of Gamma function becomes Log

Published on 06 Apr 2023 - 5:36

score 119 · Answer 5 · 2023-04-06 16:30:30

119

Views

Gamma function (for real z). Confusion to be cleared.

Published on 06 Apr 2023 - 16:30

score 97 · Answer 6 · 2026-03-25 14:22:48

97

Views

Having trouble evaluating an integral with logarithm and binomial expansion to difference of digamma functions

Published on 25 Mar 2026 - 14:22

score 204 · Answer 7 · 2026-04-01 17:32:49

204

Views

$\xi(s)=\xi(1-s)$ functional equation from $\Gamma(s)\Gamma(s+1)\zeta(s)=\int_0^\infty t^{s-1}\sum_{\alpha \in \Bbb N} \Phi_{\alpha}(t)~ dt$

Published on 01 Apr 2026 - 17:32

score 35 · Answer 8 · 2026-03-30 01:50:14

35

Views

How do I integrate this in terms of the Tricomi confluent hypergeometric function?

Published on 30 Mar 2026 - 1:50

score 86 · Answer 9 · 2026-03-27 02:35:21

86

Views

Definite integral of $\int_{-x}^{\infty} dz e^{-z^2/2} \sqrt{x+z}$

Published on 27 Mar 2026 - 2:35

score 76 · Answer 10 · 2023-04-19 02:43:03

76

Views

Big O subscript notation

Published on 19 Apr 2023 - 2:43

score 69 · Answer 11 · 2026-04-02 22:12:23

69

Views

The inverse mellin transform of the reciprocal of the Archimedean factor of the Zeta function

Published on 02 Apr 2026 - 22:12

score 81 · Answer 12 · 2026-03-27 02:33:11

81

Views

Integrals involving Gamma Functions

Published on 27 Mar 2026 - 2:33

score 173 · Answer 13 · 2023-04-25 15:59:04

173

Views

How to compute $\Gamma\left(\frac{3}{4}\right)$?

Published on 25 Apr 2023 - 15:59

score 38 · Answer 14 · 2023-04-28 15:06:05

38

Views

Strange function behaving like a Gaussian function .

Published on 28 Apr 2023 - 15:06

score 135 · Answer 15 · 2026-03-25 17:25:03

135

Views

Calculating an inverse Mellin transform

Published on 25 Mar 2026 - 17:25

List Question

What is the sum of the series $\sum_{r = 1}^{n-1}{1 \over r \sqrt[a]{\log \big(\frac{\log n}{\log r}\big)}}$?

What is $\lim_{x\to \infty}f(x)=\lim_{x\to \infty}\int_{0}^{x}\prod_{n=1}^{\infty}\left(1-e^{-t-n}\right)dt-x+1$

How can I evaluate this infinite sum?

Limit of Gamma function becomes Log

Gamma function (for real z). Confusion to be cleared.

Having trouble evaluating an integral with logarithm and binomial expansion to difference of digamma functions

$\xi(s)=\xi(1-s)$ functional equation from $\Gamma(s)\Gamma(s+1)\zeta(s)=\int_0^\infty t^{s-1}\sum_{\alpha \in \Bbb N} \Phi_{\alpha}(t)~ dt$

How do I integrate this in terms of the Tricomi confluent hypergeometric function?

Definite integral of $\int_{-x}^{\infty} dz e^{-z^2/2} \sqrt{x+z}$

Big O subscript notation

The inverse mellin transform of the reciprocal of the Archimedean factor of the Zeta function

Integrals involving Gamma Functions

How to compute $\Gamma\left(\frac{3}{4}\right)$?

Strange function behaving like a Gaussian function .

Calculating an inverse Mellin transform

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