Question

Evaluate the following series sum.

score 82 · Answer 1 · 2021-05-31 10:41:09

82

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Evaluate the following series sum.

Published on 31 May 2021 - 10:41

score 364 · Answer 2 · 2021-06-03 14:24:01

364

Views

Closed form of the sum $s_4 = \sum_{n=1}^{\infty}(-1)^n \frac{H_{n}}{(2n+1)^4}$

Published on 03 Jun 2021 - 14:24

score 211 · Answer 3 · 2021-06-04 05:26:29

211

Views

Does $\int_0^{2\pi}\frac{d\phi}{2\pi} \,\ln\left(\frac{\cos^2\phi}{C^2}\right)\,\ln\left(1-\frac{\cos^2\phi}{C^2}\right)$ have a closed form?

Published on 04 Jun 2021 - 5:26

score 84 · Answer 4 · 2021-06-08 15:27:51

84

Views

A Logarithmic Definite Integral Problem

Published on 08 Jun 2021 - 15:27

score 243 · Answer 5 · 2021-06-09 10:57:02

243

Views

Is there a closed-form for $\sum _{k=1}^{\infty }\frac{\operatorname{Si}\left(k\right)}{k^2}$?

Published on 09 Jun 2021 - 10:57

score 108 · Answer 6 · 2026-03-26 08:09:07

108

Views

The rate of convergence of the remainder of the power series for the Polylog function

Published on 26 Mar 2026 - 8:09

score 195 · Answer 7 · 2021-06-16 21:11:05

195

Views

Iterated integral involving polylogarithms

Published on 16 Jun 2021 - 21:11

score 251 · Answer 8 · 2021-06-19 21:39:36

251

Views

Arctan integral $ \int_{0}^{\infty}\frac{\arctan(x)}{x^{2}+k^{2}}$

Published on 19 Jun 2021 - 21:39

score 111 · Answer 9 · 2021-06-26 20:39:02

111

Views

Closed form evaluation of a class of inverse hyperbolic integrals

Published on 26 Jun 2021 - 20:39

score 275 · Answer 10 · 2021-06-26 22:06:18

275

Views

How can I evaluate $\int _0^1\frac{\operatorname{Li}_2\left(-x^2\right)}{\sqrt{1-x^2}}\:\mathrm{d}x$

Published on 26 Jun 2021 - 22:06

score 464 · Answer 11 · 2021-06-29 04:24:34

464

Views

Generating function of the polylogarithm.

Published on 29 Jun 2021 - 4:24

score 213 · Answer 12 · 2021-07-04 22:59:54

213

Views

Finding a closed-form for the sum $\sum_{n=1}^{\infty}\frac{\left(-1\right)^{n}H_{2n}}{n^{4}}$

Published on 04 Jul 2021 - 22:59

score 412 · Answer 13 · 2021-07-05 07:56:37

412

Views

Integral $\int _0^1\frac{\ln \left(x\right)\text{Li}_2\left(x\right)}{x\left(4\pi ^2+\ln ^2\left(x\right)\right)}\:\mathrm{d}x$

Published on 05 Jul 2021 - 7:56

score 337 · Answer 14 · 2021-07-12 23:36:23

337

Views

evaluate $\int_{0}^{1}\frac{\text{Li}_2(\frac{x^2-1}{4})}{1-x^2}dx$

Published on 12 Jul 2021 - 23:36

score 284 · Answer 15 · 2021-08-29 14:11:53

284

Views

Evaluate $\int_{1}^{\infty}\frac{\operatorname{Li}_3(-x)\ln(x-1)}{1+x^2}\text{d}x$

Published on 29 Aug 2021 - 14:11

List Question

Evaluate the following series sum.

Closed form of the sum $s_4 = \sum_{n=1}^{\infty}(-1)^n \frac{H_{n}}{(2n+1)^4}$

Does $\int_0^{2\pi}\frac{d\phi}{2\pi} \,\ln\left(\frac{\cos^2\phi}{C^2}\right)\,\ln\left(1-\frac{\cos^2\phi}{C^2}\right)$ have a closed form?

A Logarithmic Definite Integral Problem

Is there a closed-form for $\sum _{k=1}^{\infty }\frac{\operatorname{Si}\left(k\right)}{k^2}$?

The rate of convergence of the remainder of the power series for the Polylog function

Iterated integral involving polylogarithms

Arctan integral $ \int_{0}^{\infty}\frac{\arctan(x)}{x^{2}+k^{2}}$

Closed form evaluation of a class of inverse hyperbolic integrals

How can I evaluate $\int _0^1\frac{\operatorname{Li}_2\left(-x^2\right)}{\sqrt{1-x^2}}\:\mathrm{d}x$

Generating function of the polylogarithm.

Finding a closed-form for the sum $\sum_{n=1}^{\infty}\frac{\left(-1\right)^{n}H_{2n}}{n^{4}}$

Integral $\int _0^1\frac{\ln \left(x\right)\text{Li}_2\left(x\right)}{x\left(4\pi ^2+\ln ^2\left(x\right)\right)}\:\mathrm{d}x$

evaluate $\int_{0}^{1}\frac{\text{Li}_2(\frac{x^2-1}{4})}{1-x^2}dx$

Evaluate $\int_{1}^{\infty}\frac{\operatorname{Li}_3(-x)\ln(x-1)}{1+x^2}\text{d}x$

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