Question

Value of $\displaystyle\sum_{k=1}^{+\infty} \log(1+\dfrac{z}{k})-\dfrac{z}{k}$

score 77 · Answer 1 · 2022-07-07 13:24:47

77

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Value of $\displaystyle\sum_{k=1}^{+\infty} \log(1+\dfrac{z}{k})-\dfrac{z}{k}$

Published on 07 Jul 2022 - 13:24

score 73 · Answer 2 · 2026-03-28 01:46:12

73

Views

Not getting the right answer in $\zeta(0)$

Published on 28 Mar 2026 - 1:46

score 94 · Answer 3 · 2026-03-26 22:55:35

94

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Equating coefficients of $ \sum_{n \ge 1} \frac{a_n}{n^s} = \sum_{n \ge 1} \frac{b_n}{n^s}, $

Published on 26 Mar 2026 - 22:55

score 645 · Answer 4 · 2022-07-26 22:50:27

645

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Tough integral: $\int_0^1 \frac{\arctan(x^{3+\sqrt{8}})}{1+x^2}dx$

Published on 26 Jul 2022 - 22:50

score 284 · Answer 5 · 2022-08-04 02:08:08

284

Views

Is there any other method to show that $\int_{0}^{\frac{\pi}{2}} x \ln (\sin x) d x =-\frac{\pi^{2}}{8} \ln 2+\frac{7}{16}\zeta(3)?$

Published on 04 Aug 2022 - 2:08

score 131 · Answer 6 · 2022-08-28 01:59:30

131

Views

Hardy’s work about zeta function

Published on 28 Aug 2022 - 1:59

score 45 · Answer 7 · 2022-09-16 12:24:45

45

Views

Deducing local bound from global bound for zeros of Riemann $\zeta(s)$

Published on 16 Sep 2022 - 12:24

score 342 · Answer 8 · 2022-09-28 20:40:54

342

Views

Evaluating Accelerator's integral $\int_0^{\infty} \frac{e^{4x}-e^{2x}}{x(e^{2x}+1)^3}dx$

Published on 28 Sep 2022 - 20:40

score 172 · Answer 9 · 2022-09-29 04:13:05

172

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What happens when an even natural number $n$ meets the integral $\int_{0}^{\frac{\pi}{2}} x\tan 2 x \ln^n (\tan x) d x$?

Published on 29 Sep 2022 - 4:13

score 230 · Answer 10 · 2022-10-01 10:19:55

Challenge:$ \int_0^{\infty} \frac{e^{2x}-e^{x}}{x(e^{2x}+1)^2}dx=3\ln A +\frac{C}{\pi}- (1/4)-\frac{\ln2}{3}-\frac{\ln\pi}{2}+\ln\Gamma(\frac{3}{4})$

score 44 · Answer 11 · 2022-10-07 09:29:45

44

Views

Number of points on elliptic curve $E:y^2 = x^3 +1$ over $\mathbb{F}_q$ with $q = p^n$ and $p\equiv 1 \mod 3$ for $p>3$

Published on 07 Oct 2022 - 9:29

score 240 · Answer 12 · 2026-03-25 07:44:51

240

Views

Mellin transform of theta function $\theta$ to show $\zeta(-1)=-\frac{1}{12}$

Published on 25 Mar 2026 - 7:44

score 62 · Answer 13 · 2026-03-28 03:26:02

62

Views

analytic continuation of the spectral zeta function

Published on 28 Mar 2026 - 3:26

score 101 · Answer 14 · 2022-11-02 09:58:20

101

Views

Find the sum of the diverge series $\sum_{n=1}^{\infty}n^n$

Published on 02 Nov 2022 - 9:58

score 85 · Answer 15 · 2022-11-05 18:25:39

85

Views

Does this function have triple log behavior?

Published on 05 Nov 2022 - 18:25

List Question

Value of $\displaystyle\sum_{k=1}^{+\infty} \log(1+\dfrac{z}{k})-\dfrac{z}{k}$

Not getting the right answer in $\zeta(0)$

Equating coefficients of $ \sum_{n \ge 1} \frac{a_n}{n^s} = \sum_{n \ge 1} \frac{b_n}{n^s}, $

Tough integral: $\int_0^1 \frac{\arctan(x^{3+\sqrt{8}})}{1+x^2}dx$

Is there any other method to show that $\int_{0}^{\frac{\pi}{2}} x \ln (\sin x) d x =-\frac{\pi^{2}}{8} \ln 2+\frac{7}{16}\zeta(3)?$

Hardy’s work about zeta function

Deducing local bound from global bound for zeros of Riemann $\zeta(s)$

Evaluating Accelerator's integral $\int_0^{\infty} \frac{e^{4x}-e^{2x}}{x(e^{2x}+1)^3}dx$

What happens when an even natural number $n$ meets the integral $\int_{0}^{\frac{\pi}{2}} x\tan 2 x \ln^n (\tan x) d x$?

Challenge:$ \int_0^{\infty} \frac{e^{2x}-e^{x}}{x(e^{2x}+1)^2}dx=3\ln A +\frac{C}{\pi}- (1/4)-\frac{\ln2}{3}-\frac{\ln\pi}{2}+\ln\Gamma(\frac{3}{4})$

Number of points on elliptic curve $E:y^2 = x^3 +1$ over $\mathbb{F}_q$ with $q = p^n$ and $p\equiv 1 \mod 3$ for $p>3$

Mellin transform of theta function $\theta$ to show $\zeta(-1)=-\frac{1}{12}$

analytic continuation of the spectral zeta function

Find the sum of the diverge series $\sum_{n=1}^{\infty}n^n$

Does this function have triple log behavior?

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