Question

Evaluation of a log-trig integral in terms of the Clausen function (or other functions related to the dilogarithm)

score 222 · Answer 1 · 2026-03-27 01:04:19

222

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Evaluation of a log-trig integral in terms of the Clausen function (or other functions related to the dilogarithm)

Published on 27 Mar 2026 - 1:04

score 83 · Answer 2 · 2026-03-26 04:53:54

83

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Number of subsets $S \subset A_1 \cup A_2 \cup ... A_n$ where $|S \cap A_i| = a_i$?

Published on 26 Mar 2026 - 4:53

score 157 · Answer 3 · 2026-03-25 16:14:05

157

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Does this $\int_{0}^{\infty}(\frac{\log x}{e^x})^n dx$ always have a closed form for $n$ being positive integer ? what about its irrationality?

Published on 25 Mar 2026 - 16:14

score 83 · Answer 4 · 2026-02-23 12:09:15

83

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Is there a formula for $f(x)$ where $f(x)=$ the sum all simplest fractions with the numerator$+$denominator equals $x$

Published on 23 Feb 2026 - 12:09

score 83 · Answer 5 · 2026-03-27 04:38:40

83

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Closed-form expressions for the zeros of $\text{Li}_{-n}(x)$?

Published on 27 Mar 2026 - 4:38

score 157 · Answer 6 · 2026-03-28 20:59:14

157

Views

Closed form of $\sqrt{2 + \sqrt{2 + ... + \sqrt{2 + \sqrt{x}}}}$

Published on 28 Mar 2026 - 20:59

score 189 · Answer 7 · 2020-07-18 13:16:11

What is the closed form of the sequence $\{-\frac12,\frac19,\frac{13}{100},\frac{71}{588},\frac{71}{648},\frac{1447}{14520},\frac{617}{6760},...\}$?

score 159 · Answer 8 · 2026-03-30 14:43:31

159

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Evaluating the power series of the multifactorial reciprocal $\sum_{n=0}^\infty \frac{x^n}{n!!...!!}$

Published on 30 Mar 2026 - 14:43

score 77 · Answer 9 · 2020-07-18 22:35:08

77

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Find an expression whose derivative is multiplicatively separable?

Published on 18 Jul 2020 - 22:35

score 45 · Answer 10 · 2020-07-19 09:04:58

45

Views

Is there a closed form for the sum $\sum_{k=1}^\infty \frac{H_k}{1+2k}x^{1+2k}$?

Published on 19 Jul 2020 - 9:04

score 237 · Answer 11 · 2026-03-27 05:38:09

237

Views

Time complexity of CAS integration algorithms. Can we always integrate the integrable expressions with guaranteed closed form solutions?

Published on 27 Mar 2026 - 5:38

score 3.3k · Answer 12 · 2026-03-27 02:59:30

3.3k

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Remarkable logarithmic integral $\int_0^1 \frac{\log^2 (1-x) \log^2 x \log^3(1+x)}{x}dx$

Published on 27 Mar 2026 - 2:59

score 363 · Answer 13 · 2020-07-21 23:04:10

363

Views

General integral $\int_0^{\frac{\pi}{p}}\ln\tan x \,dx $

Published on 21 Jul 2020 - 23:04

score 174 · Answer 14 · 2026-03-29 08:57:56

174

Views

Closed-form expression for $\prod_{n=0}^{\infty}\frac{(4n+3)^{1/(4n+3)}}{(4n+5)^{1/(4n+5)}}$?

Published on 29 Mar 2026 - 8:57

score 248 · Answer 15 · 2026-03-23 12:45:53

248

Views

An easier evaluation of $\det\limits_{1\leqslant i,j\leqslant n}\left\{\frac{x_i-x_j}{x_i+x_j}\right\}$

Published on 23 Mar 2026 - 12:45

List Question

Evaluation of a log-trig integral in terms of the Clausen function (or other functions related to the dilogarithm)

Number of subsets $S \subset A_1 \cup A_2 \cup ... A_n$ where $|S \cap A_i| = a_i$?

Does this $\int_{0}^{\infty}(\frac{\log x}{e^x})^n dx$ always have a closed form for $n$ being positive integer ? what about its irrationality?

Is there a formula for $f(x)$ where $f(x)=$ the sum all simplest fractions with the numerator$+$denominator equals $x$

Closed-form expressions for the zeros of $\text{Li}_{-n}(x)$?

Closed form of $\sqrt{2 + \sqrt{2 + ... + \sqrt{2 + \sqrt{x}}}}$

What is the closed form of the sequence $\{-\frac12,\frac19,\frac{13}{100},\frac{71}{588},\frac{71}{648},\frac{1447}{14520},\frac{617}{6760},...\}$?

Evaluating the power series of the multifactorial reciprocal $\sum_{n=0}^\infty \frac{x^n}{n!!...!!}$

Find an expression whose derivative is multiplicatively separable?

Is there a closed form for the sum $\sum_{k=1}^\infty \frac{H_k}{1+2k}x^{1+2k}$?

Time complexity of CAS integration algorithms. Can we always integrate the integrable expressions with guaranteed closed form solutions?

Remarkable logarithmic integral $\int_0^1 \frac{\log^2 (1-x) \log^2 x \log^3(1+x)}{x}dx$

General integral $\int_0^{\frac{\pi}{p}}\ln\tan x \,dx $

Closed-form expression for $\prod_{n=0}^{\infty}\frac{(4n+3)^{1/(4n+3)}}{(4n+5)^{1/(4n+5)}}$?

An easier evaluation of $\det\limits_{1\leqslant i,j\leqslant n}\left\{\frac{x_i-x_j}{x_i+x_j}\right\}$

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