List questions from polylogarithm

Published on 16 Feb 2016 - 12:22

942

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Proving that $\int_0^1 \frac{\log^2(x)\tanh^{-1}(x)}{1+x^2}dx=\beta(4)-\frac{\pi^2}{12}G$

Published on 25 Mar 2016 - 8:14

343

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Integral $\int_0^1\frac{\ln(1-x)}{x}\text{Li}_3\left({x} \right)\,dx$

Published on 29 Mar 2016 - 7:25

401

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Evaluating Fermi Dirac integrals of order j<0

Published on 25 Mar 2026 - 10:53

1.7k

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Sum of $k^2*x^k$

Published on 25 Mar 2026 - 4:25

667

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Integration of a polylogarithm: Is this function known?

Published on 03 May 2016 - 13:39

1.2k

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Show that $\sum_{n=0}^{\infty}\frac{2^n(5n^5+5n^4+5n^3+5n^2-9n+9)}{(2n+1)(2n+2)(2n+3){2n\choose n}}=\frac{9\pi^2}{8}$

Published on 27 Mar 2026 - 16:22

148

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Complex logarithms when computing real-valued integral

Published on 26 May 2016 - 3:00

98

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What's the worst sequence that still leads to a converging series?

Published on 30 May 2016 - 21:59

868

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Evaluate $ \int_{0}^{1} \log\left(\frac{x^2-2x-4}{x^2+2x-4}\right) \frac{\mathrm{d}x}{\sqrt{1-x^2}} $

Published on 15 Jun 2016 - 16:09

2k

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A very difficult integral involving integration by parts.

Published on 26 Mar 2026 - 16:26

555

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Is the following Harmonic Number Identity true?

Published on 02 Jul 2016 - 22:57

735

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Prove $\int_{\frac{\pi}{20}}^{\frac{3\pi}{20}} \ln \tan x\,\,dx= - \frac{2G}{5}$

Published on 03 Jul 2016 - 17:40

266

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Tough quadrilogarithm integral

Published on 07 Aug 2013 - 1:15

1.7k

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Definite Dilogarithm integral $\int^1_0 \frac{\operatorname{Li}_2^2(x)}{x}\, dx $

Published on 08 Aug 2013 - 0:28

List Question

The function $\mathrm{Li}_2(x)=\int_2^x\frac{dt}{\log^2t}$, its inverse and summation

Proving that $\int_0^1 \frac{\log^2(x)\tanh^{-1}(x)}{1+x^2}dx=\beta(4)-\frac{\pi^2}{12}G$

Integral $\int_0^1\frac{\ln(1-x)}{x}\text{Li}_3\left({x} \right)\,dx$

Evaluating Fermi Dirac integrals of order j<0

Sum of $k^2*x^k$

Integration of a polylogarithm: Is this function known?

Show that $\sum_{n=0}^{\infty}\frac{2^n(5n^5+5n^4+5n^3+5n^2-9n+9)}{(2n+1)(2n+2)(2n+3){2n\choose n}}=\frac{9\pi^2}{8}$

Complex logarithms when computing real-valued integral

What's the worst sequence that still leads to a converging series?

Evaluate $ \int_{0}^{1} \log\left(\frac{x^2-2x-4}{x^2+2x-4}\right) \frac{\mathrm{d}x}{\sqrt{1-x^2}} $

A very difficult integral involving integration by parts.

Is the following Harmonic Number Identity true?

Prove $\int_{\frac{\pi}{20}}^{\frac{3\pi}{20}} \ln \tan x\,\,dx= - \frac{2G}{5}$

Tough quadrilogarithm integral

Definite Dilogarithm integral $\int^1_0 \frac{\operatorname{Li}_2^2(x)}{x}\, dx $

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