List questions from polylogarithm

Published on 21 Jan 2022 - 13:01

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A generalized "Rare" integral involving $\operatorname{Li}_3$

Published on 23 Jan 2022 - 6:41

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General expressions for $\mathcal{L}(n)=\int_{0}^{\infty}\operatorname{Ci}(x)^n\text{d}x$

Published on 31 Jan 2022 - 14:58

120

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Sum of Fermi-Dirac integrals with opposite chemical potentials: closed form (Le Bellac eq. 1.13)

Published on 25 Mar 2026 - 12:20

150

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Integral involving product of dilogarithm and an exponential

Published on 02 Feb 2022 - 18:19

114

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Closed-form for $\int_0^{a^2} \mathrm{Ei} (-s) \frac{1 - e^s}{s} ds$

Published on 03 Feb 2022 - 17:54

395

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Proving $\int_0^{1/2}\frac{\text{Li}_2(-x)}{1-x}dx=-\text{Li}_3\left(-\frac12\right)-\frac{13}{24}\zeta(3)$

Published on 08 Feb 2022 - 10:10

215

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Can this formula for $\zeta(3)$ be proven or simplified further?

Published on 25 Mar 2026 - 11:54

148

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Evaluate: ${{\int_{0}^{1}\frac{\ln(1+x)^5}{x+2}dx-\int_{0}^{1}\frac{\ln(1+x)^5}{x+3}dx+5\ln2\int_{0}^{1}\frac{\ln(1+x)^4}{x+3}dx}}$

Published on 14 Feb 2022 - 12:39

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Are these generalizations known in the literature?

Published on 06 Mar 2022 - 6:37

146

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Evaluating improper integral $\int_0^1 \frac{\log(x)}{x+\alpha}\; dx$ for small positive $\alpha$

Published on 12 Mar 2022 - 3:53

41

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Canonical reference for algebraic theory of polylogs?

Published on 28 Mar 2026 - 4:24

126

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Closed form for $\rm{Li }_2\left( -{\frac {i\sqrt {3}}{3}} \right)$

Published on 25 Mar 2026 - 20:42

128

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Series expansion of $\text{Li}_3(1-x)$ at $x \sim 0$

Published on 13 Apr 2022 - 13:37

51

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How is $(2^a)^{\lg n} = n^a$?

Published on 20 Apr 2022 - 14:58

List Question

A rare integral involving $\operatorname{Li}_2$

A generalized "Rare" integral involving $\operatorname{Li}_3$

General expressions for $\mathcal{L}(n)=\int_{0}^{\infty}\operatorname{Ci}(x)^n\text{d}x$

Sum of Fermi-Dirac integrals with opposite chemical potentials: closed form (Le Bellac eq. 1.13)

Integral involving product of dilogarithm and an exponential

Closed-form for $\int_0^{a^2} \mathrm{Ei} (-s) \frac{1 - e^s}{s} ds$

Proving $\int_0^{1/2}\frac{\text{Li}_2(-x)}{1-x}dx=-\text{Li}_3\left(-\frac12\right)-\frac{13}{24}\zeta(3)$

Can this formula for $\zeta(3)$ be proven or simplified further?

Evaluate: ${{\int_{0}^{1}\frac{\ln(1+x)^5}{x+2}dx-\int_{0}^{1}\frac{\ln(1+x)^5}{x+3}dx+5\ln2\int_{0}^{1}\frac{\ln(1+x)^4}{x+3}dx}}$

Are these generalizations known in the literature?

Evaluating improper integral $\int_0^1 \frac{\log(x)}{x+\alpha}\; dx$ for small positive $\alpha$

Canonical reference for algebraic theory of polylogs?

Closed form for $\rm{Li }_2\left( -{\frac {i\sqrt {3}}{3}} \right)$

Series expansion of $\text{Li}_3(1-x)$ at $x \sim 0$

How is $(2^a)^{\lg n} = n^a$?

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