Question

The closed form for $\sum_{n=1}^\infty \frac{H_{n/2}}{n^2}x^n$

score 277 · Answer 1 · 2020-03-14 23:09:33

277

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The closed form for $\sum_{n=1}^\infty \frac{H_{n/2}}{n^2}x^n$

Published on 14 Mar 2020 - 23:09

score 203 · Answer 2 · 2020-03-16 07:31:12

203

Views

Approaching $\sum_{n=1}^\infty\frac{\overline{H}_n-H_{n/2}}{n^3}$ elegantly

Published on 16 Mar 2020 - 7:31

score 136 · Answer 3 · 2020-03-26 23:09:56

136

Views

Different approach to compute $\int_0^1\frac{\ln(x)}{1+x}\text{Li}_2\left(\frac{1+x}2\right)\ dx$

Published on 26 Mar 2020 - 23:09

score 100 · Answer 4 · 2026-03-25 20:36:14

100

Views

Integral $\int_{0}^{e} \frac{\operatorname{W(x)} - x}{\operatorname{W(x)} + x} dx$

Published on 25 Mar 2026 - 20:36

score 112 · Answer 5 · 2020-04-02 03:37:16

112

Views

Estimate of integral of Fourier series

Published on 02 Apr 2020 - 3:37

score 59 · Answer 6 · 2020-04-03 21:30:52

59

Views

Is that series $\sum_{k=1}^{\infty}\frac{z^k}{ak + 1}$ related to a common function?

Published on 03 Apr 2020 - 21:30

score 659 · Answer 7 · 2020-04-06 06:15:10

659

Views

Evaluate $\sum _{n=1}^{\infty } \frac{1}{n^5 2^n \binom{3 n}{n}}$ in terms of elementary constants

Published on 06 Apr 2020 - 6:15

score 133 · Answer 8 · 2020-04-06 23:51:05

133

Views

Analytically solving (finding a maxima) a system of equations involving PolyLog functions (Fermi-Dirac Integrals)

Published on 06 Apr 2020 - 23:51

score 181 · Answer 9 · 2026-03-26 01:56:51

181

Views

Polylog identities

Published on 26 Mar 2026 - 1:56

score 211 · Answer 10 · 2020-04-19 12:17:26

211

Views

prove that $\int_{0}^{1}\Big(\frac{\operatorname{li}(x)}{x}\Big)^2dx= \frac{\pi^2}{6}$

Published on 19 Apr 2020 - 12:17

score 180 · Answer 11 · 2020-04-20 17:15:54

180

Views

How to simplify this polylog expression $\operatorname{Li}_4\left(\frac{z-1}{z}\right)$?

Published on 20 Apr 2020 - 17:15

score 51 · Answer 12 · 2020-04-24 09:39:25

51

Views

Generalized series involving harmonic numbers

Published on 24 Apr 2020 - 9:39

score 365 · Answer 13 · 2020-04-24 18:25:32

365

Views

Evaluate $\int_0^1 \frac{x \operatorname{Li}_2(x) \log (1+x)}{x^2+1} \, dx$

Published on 24 Apr 2020 - 18:25

score 95 · Answer 14 · 2026-03-25 19:08:31

95

Views

dilogarithm property.

Published on 25 Mar 2026 - 19:08

score 294 · Answer 15 · 2020-05-02 12:07:49

294

Views

Computing $\int_0^1\frac{1-2x}{2x^2-2x+1}\ln(x)\text{Li}_2(x)dx$

Published on 02 May 2020 - 12:07

List Question

The closed form for $\sum_{n=1}^\infty \frac{H_{n/2}}{n^2}x^n$

Approaching $\sum_{n=1}^\infty\frac{\overline{H}_n-H_{n/2}}{n^3}$ elegantly

Different approach to compute $\int_0^1\frac{\ln(x)}{1+x}\text{Li}_2\left(\frac{1+x}2\right)\ dx$

Integral $\int_{0}^{e} \frac{\operatorname{W(x)} - x}{\operatorname{W(x)} + x} dx$

Estimate of integral of Fourier series

Is that series $\sum_{k=1}^{\infty}\frac{z^k}{ak + 1}$ related to a common function?

Evaluate $\sum _{n=1}^{\infty } \frac{1}{n^5 2^n \binom{3 n}{n}}$ in terms of elementary constants

Analytically solving (finding a maxima) a system of equations involving PolyLog functions (Fermi-Dirac Integrals)

Polylog identities

prove that $\int_{0}^{1}\Big(\frac{\operatorname{li}(x)}{x}\Big)^2dx= \frac{\pi^2}{6}$

How to simplify this polylog expression $\operatorname{Li}_4\left(\frac{z-1}{z}\right)$?

Generalized series involving harmonic numbers

Evaluate $\int_0^1 \frac{x \operatorname{Li}_2(x) \log (1+x)}{x^2+1} \, dx$

dilogarithm property.

Computing $\int_0^1\frac{1-2x}{2x^2-2x+1}\ln(x)\text{Li}_2(x)dx$

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