Question

Why is $\lim\limits_{x\to\infty}\frac{\sum_{i=1}^x(\sum_{j=1}^i\frac1j-\ln i-\gamma)}{\sum_{i=1}^x\frac1i}=\frac12$?

score 207 · Answer 1 · 2021-06-19 10:47:38

207

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Why is $\lim\limits_{x\to\infty}\frac{\sum_{i=1}^x(\sum_{j=1}^i\frac1j-\ln i-\gamma)}{\sum_{i=1}^x\frac1i}=\frac12$?

Published on 19 Jun 2021 - 10:47

score 126 · Answer 2 · 2021-06-29 06:44:15

126

Views

Sum of 1.5-powers of natural numbers using Euler-Maclaurin Formula?

Published on 29 Jun 2021 - 6:44

score 149 · Answer 3 · 2026-03-26 12:40:22

149

Views

What are some interesting problems in the intersection of Diophantine Approx and Algebraic Geometry?

Published on 26 Mar 2026 - 12:40

score 102 · Answer 4 · 2021-06-29 17:36:16

102

Views

What is an approximate closed form for sum of $n^n$ series?

Published on 29 Jun 2021 - 17:36

score 199 · Answer 5 · 2021-06-30 05:14:32

199

Views

Closed form of sum of n^n series?

Published on 30 Jun 2021 - 5:14

score 213 · Answer 6 · 2021-07-01 04:27:12

213

Views

How to derive Euler-Maclaurin sum formula from Taylor Series?

Published on 01 Jul 2021 - 4:27

score 165 · Answer 7 · 2021-07-03 20:59:43

165

Views

Intermediate step in deriving integral representation of Euler–Mascheroni constant: $\int_0^1\frac{1-e^{-t}-e^{-1/t}}{t}dt$

Published on 03 Jul 2021 - 20:59

score 128 · Answer 8 · 2021-07-20 15:54:42

128

Views

How to derive this series for $\gamma$ that is only involving odd integer values of $\zeta(s)$?

Published on 20 Jul 2021 - 15:54

score 34 · Answer 9 · 2021-07-25 07:41:51

34

Views

Explaining Algebraic Independence of $\delta$ and $\gamma$

Published on 25 Jul 2021 - 7:41

score 222 · Answer 10 · 2021-08-07 14:52:14

222

Views

Does $\sum_{n=1}^\infty \frac{1}{nH_n^2}$ (& related) have any closed form representaions?

Published on 07 Aug 2021 - 14:52

score 183 · Answer 11 · 2021-08-09 05:40:17

183

Views

On the irrationality of Euler Mascheroni constant

Published on 09 Aug 2021 - 5:40

score 66 · Answer 12 · 2021-08-09 07:08:12

66

Views

Seeking reference on a fact involving Euler's constant and the reciprocal of a uniform

Published on 09 Aug 2021 - 7:08

score 117 · Answer 13 · 2021-08-17 14:00:47

117

Views

Evaluate a $\gamma$ integral

Published on 17 Aug 2021 - 14:00

score 45 · Answer 14 · 2021-10-19 18:34:24

45

Views

Little-o of a summation

Published on 19 Oct 2021 - 18:34

score 694 · Answer 15 · 2021-10-20 23:37:22

694

Views

Proof that the limit of a series of exponential distributed random variables follows a Gumbel distribution

Published on 20 Oct 2021 - 23:37

List Question

Why is $\lim\limits_{x\to\infty}\frac{\sum_{i=1}^x(\sum_{j=1}^i\frac1j-\ln i-\gamma)}{\sum_{i=1}^x\frac1i}=\frac12$?

Sum of 1.5-powers of natural numbers using Euler-Maclaurin Formula?

What are some interesting problems in the intersection of Diophantine Approx and Algebraic Geometry?

What is an approximate closed form for sum of $n^n$ series?

Closed form of sum of n^n series?

How to derive Euler-Maclaurin sum formula from Taylor Series?

Intermediate step in deriving integral representation of Euler–Mascheroni constant: $\int_0^1\frac{1-e^{-t}-e^{-1/t}}{t}dt$

How to derive this series for $\gamma$ that is only involving odd integer values of $\zeta(s)$?

Explaining Algebraic Independence of $\delta$ and $\gamma$

Does $\sum_{n=1}^\infty \frac{1}{nH_n^2}$ (& related) have any closed form representaions?

On the irrationality of Euler Mascheroni constant

Seeking reference on a fact involving Euler's constant and the reciprocal of a uniform

Evaluate a $\gamma$ integral

Little-o of a summation

Proof that the limit of a series of exponential distributed random variables follows a Gumbel distribution

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