Question

Generating function of Clausen functions: $\displaystyle\sum_{n=1}^\infty \text{Cl}_{2n}(x)\frac{t^{2n}}{(2n)!}$

score 120 · Answer 1 · 2023-12-11 13:35:07

120

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Generating function of Clausen functions: $\displaystyle\sum_{n=1}^\infty \text{Cl}_{2n}(x)\frac{t^{2n}}{(2n)!}$

Published on 11 Dec 2023 - 13:35

score 181 · Answer 2 · 2023-12-14 15:48:00

181

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Approximation for $\sum_{i=1}^\infty \frac{\sqrt i}{\sqrt{2\pi \epsilon}} e^{\frac{-i}{2\epsilon}}$?

Published on 14 Dec 2023 - 15:48

score 33 · Answer 3 · 2023-12-17 02:36:18

33

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Regularization involving Stieltjes constants: $\displaystyle\sum_{k=1}^{\infty}\frac{\ln(k)^n}{k}\overset{\mathcal{R}}{=}\gamma_n$

Published on 17 Dec 2023 - 2:36

score 46 · Answer 4 · 2023-12-30 06:37:43

46

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Contour integration with polylogarithm

Published on 30 Dec 2023 - 6:37

score 152 · Answer 5 · 2024-01-03 16:07:18

152

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$\displaystyle\int_{0}^{\frac{\pi}{2}}\ln(1+\alpha^N\tan(x)^N)\mathrm{d}x\quad$ where $N\in\mathbb{N}$

Published on 03 Jan 2024 - 16:07

score 1k · Answer 6 · 2024-01-06 19:19:16

1k

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Solution of a meme integral: $\int \frac{x \sin(x)}{1+\cos(x)^2}\mathrm{d}x$

Published on 06 Jan 2024 - 19:19

score 21 · Answer 7 · 2024-01-09 13:06:34

21

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Upper bound of a polylogarithm type series

Published on 09 Jan 2024 - 13:06

score 131 · Answer 8 · 2024-01-22 08:33:37

131

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I need help evaluating the integral $\int_{-\infty}^{\infty} \frac{\log(1+e^{-z})}{1+e^{-z}}dz$

Published on 22 Jan 2024 - 8:33

score 60 · Answer 9 · 2024-02-01 15:05:39

60

Views

Help verifying expression involving dilogarithms.

Published on 01 Feb 2024 - 15:05

score 177 · Answer 10 · 2024-02-13 09:01:05

177

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how to find closed form for $\int_0^1 \frac{x}{x^2+1} \left(\ln(1-x) \right)^{n-1}dx$?

Published on 13 Feb 2024 - 9:01

score 49 · Answer 11 · 2026-02-23 04:44:33

49

Views

Connection between the polylogarithm and the Bernoulli polynomials.

Published on 23 Feb 2026 - 4:44

score 33 · Answer 12 · 2024-02-15 23:59:16

33

Views

Relations between Dilogarithms and Imaginary part of Hurwitz-Zeta function

Published on 15 Feb 2024 - 23:59

score 125 · Answer 13 · 2026-03-26 22:53:35

125

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Is it possible to evaluate this integral? If not, is it possible to determine whether the result is an elliptic function or not?

Published on 26 Mar 2026 - 22:53

score 47 · Answer 14 · 2024-03-05 17:48:02

47

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How to integrate $\frac{x^N\log(1+x)}{\sqrt{x^2+x_1^2}\sqrt{x^2+x_2^2}}$?

Published on 05 Mar 2024 - 17:48

score 57 · Answer 15 · 2024-03-24 23:30:51

57

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Behaviour of polylogarithm at $|z|=1$

Published on 24 Mar 2024 - 23:30

List Question

Generating function of Clausen functions: $\displaystyle\sum_{n=1}^\infty \text{Cl}_{2n}(x)\frac{t^{2n}}{(2n)!}$

Approximation for $\sum_{i=1}^\infty \frac{\sqrt i}{\sqrt{2\pi \epsilon}} e^{\frac{-i}{2\epsilon}}$?

Regularization involving Stieltjes constants: $\displaystyle\sum_{k=1}^{\infty}\frac{\ln(k)^n}{k}\overset{\mathcal{R}}{=}\gamma_n$

Contour integration with polylogarithm

$\displaystyle\int_{0}^{\frac{\pi}{2}}\ln(1+\alpha^N\tan(x)^N)\mathrm{d}x\quad$ where $N\in\mathbb{N}$

Solution of a meme integral: $\int \frac{x \sin(x)}{1+\cos(x)^2}\mathrm{d}x$

Upper bound of a polylogarithm type series

I need help evaluating the integral $\int_{-\infty}^{\infty} \frac{\log(1+e^{-z})}{1+e^{-z}}dz$

Help verifying expression involving dilogarithms.

how to find closed form for $\int_0^1 \frac{x}{x^2+1} \left(\ln(1-x) \right)^{n-1}dx$?

Connection between the polylogarithm and the Bernoulli polynomials.

Relations between Dilogarithms and Imaginary part of Hurwitz-Zeta function

Is it possible to evaluate this integral? If not, is it possible to determine whether the result is an elliptic function or not?

How to integrate $\frac{x^N\log(1+x)}{\sqrt{x^2+x_1^2}\sqrt{x^2+x_2^2}}$?

Behaviour of polylogarithm at $|z|=1$

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