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Integrals of integer powers of dilogarithm function

score 1.1k · Answer 1 · 2026-03-26 01:27:04

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Integrals of integer powers of dilogarithm function

Published on 26 Mar 2026 - 1:27

score 301 · Answer 2 · 2026-03-25 19:10:30

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Infinite Series $\sum_{k=1}^\infty\left(\zeta(2)-\sum_{n=1}^k\frac1{n^2}\right)^2$

Published on 25 Mar 2026 - 19:10

score 1.2k · Answer 3 · 2014-08-29 16:09:59

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Integral $\int_0^{\large\frac{\pi}{4}}\left(\frac{1}{\log(\tan(x))}+\frac{1}{1-\tan(x)}\right)dx$

Published on 29 Aug 2014 - 16:09

score 311 · Answer 4 · 2014-08-29 23:48:15

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Is there closed form for $\int_0^{\pi/4}\exp(-\sum_{n=1}^{\infty}\frac{\tan^{2n}x}{n+a})\ dx$?

Published on 29 Aug 2014 - 23:48

score 737 · Answer 5 · 2026-03-28 02:05:21

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Closed-forms of infinite series with factorial in the denominator

Published on 28 Mar 2026 - 2:05

score 1.1k · Answer 6 · 2026-03-28 08:08:12

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Trigonometric functions expressed as definite integrals with Bessel functions

Published on 28 Mar 2026 - 8:08

score 428 · Answer 7 · 2014-08-31 07:05:59

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Trigonometric integral: $\int_{25\pi/4}^{53\pi/4} \frac{1}{(1+2^{\sin x})(1+2^{\cos x})}\,dx$

Published on 31 Aug 2014 - 7:05

score 1.5k · Answer 8 · 2026-03-27 23:23:32

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Simpler closed form for $\sum_{n=1}^\infty\frac{\Gamma\left(n+\frac{1}{2}\right)}{(2n+1)^4\,4^n\,n!}$

Published on 27 Mar 2026 - 23:23

score 2.6k · Answer 9 · 2014-08-31 18:58:25

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Prove $\int_{0}^{\pi/2} \ln \left(x^{2} + (\ln\cos x)^2 \right) \, dx=\pi\ln\ln2 $

Published on 31 Aug 2014 - 18:58

score 288 · Answer 10 · 2026-03-26 03:12:38

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Evaluation of a class of continued fractions

Published on 26 Mar 2026 - 3:12

score 248 · Answer 11 · 2014-09-01 17:18:22

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Why is $\int_0^{2\pi} e^{i\,k\rho[\sin\alpha\cos\alpha-\sin\theta\cos(\phi-\beta)]}\mathrm{d}\beta = 2\pi J_0(k\rho\xi)$?

Published on 01 Sep 2014 - 17:18

score 504 · Answer 12 · 2014-09-02 09:29:00

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A closed-form of product the gamma functions containing $\pi$ and $\phi$

Published on 02 Sep 2014 - 9:29

score 56 · Answer 13 · 2014-09-03 15:31:47

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simplifying an expression with even and odd integers

Published on 03 Sep 2014 - 15:31

score 6.3k · Answer 14 · 2026-03-26 01:04:41

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Closed Form for the Imaginary Part of $\text{Li}_3\Big(\frac{1+i}2\Big)$

Published on 26 Mar 2026 - 1:04

score 7k · Answer 15 · 2026-03-27 23:23:35

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Closed form for ${\large\int}_0^1\frac{\ln^2x}{\sqrt{1-x+x^2}}dx$

Published on 27 Mar 2026 - 23:23

List Question

Integrals of integer powers of dilogarithm function

Infinite Series $\sum_{k=1}^\infty\left(\zeta(2)-\sum_{n=1}^k\frac1{n^2}\right)^2$

Integral $\int_0^{\large\frac{\pi}{4}}\left(\frac{1}{\log(\tan(x))}+\frac{1}{1-\tan(x)}\right)dx$

Is there closed form for $\int_0^{\pi/4}\exp(-\sum_{n=1}^{\infty}\frac{\tan^{2n}x}{n+a})\ dx$?

Closed-forms of infinite series with factorial in the denominator

Trigonometric functions expressed as definite integrals with Bessel functions

Trigonometric integral: $\int_{25\pi/4}^{53\pi/4} \frac{1}{(1+2^{\sin x})(1+2^{\cos x})}\,dx$

Simpler closed form for $\sum_{n=1}^\infty\frac{\Gamma\left(n+\frac{1}{2}\right)}{(2n+1)^4\,4^n\,n!}$

Prove $\int_{0}^{\pi/2} \ln \left(x^{2} + (\ln\cos x)^2 \right) \, dx=\pi\ln\ln2 $

Evaluation of a class of continued fractions

Why is $\int_0^{2\pi} e^{i\,k\rho[\sin\alpha\cos\alpha-\sin\theta\cos(\phi-\beta)]}\mathrm{d}\beta = 2\pi J_0(k\rho\xi)$?

A closed-form of product the gamma functions containing $\pi$ and $\phi$

simplifying an expression with even and odd integers

Closed Form for the Imaginary Part of $\text{Li}_3\Big(\frac{1+i}2\Big)$

Closed form for ${\large\int}_0^1\frac{\ln^2x}{\sqrt{1-x+x^2}}dx$

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