Question

Beautiful closed form of $\sum_{k=0}^{\infty}\frac{(-1)^{k+1}}{2(k+1)^2}\int_0^1\ln (k+1-k^x)+2\ln (1+k^x)dx$

score 184 · Answer 1 · 2026-03-31 13:49:28

184

Views

Beautiful closed form of $\sum_{k=0}^{\infty}\frac{(-1)^{k+1}}{2(k+1)^2}\int_0^1\ln (k+1-k^x)+2\ln (1+k^x)dx$

Published on 31 Mar 2026 - 13:49

score 307 · Answer 2 · 2020-07-13 20:04:20

307

Views

On Logarithmic Derivative transformation

Published on 13 Jul 2020 - 20:04

score 106 · Answer 3 · 2020-07-14 09:56:20

106

Views

On the series $\sum_{n=-\infty}^{\infty} \frac{\cos nx}{\Gamma\left ( a+n+1 \right ) \Gamma \left ( a-n+1 \right )}$

Published on 14 Jul 2020 - 9:56

score 117 · Answer 4 · 2026-03-29 07:36:27

117

Views

value of lommel function for negative first parameter and positive second parameter

Published on 29 Mar 2026 - 7:36

score 367 · Answer 5 · 2020-07-15 23:16:00

367

Views

Equality of the Schläfli's integrals

Published on 15 Jul 2020 - 23:16

score 80 · Answer 6 · 2026-03-26 20:12:22

80

Views

representation through special numbers

Published on 26 Mar 2026 - 20:12

score 83 · Answer 7 · 2026-03-27 04:38:40

83

Views

Closed-form expressions for the zeros of $\text{Li}_{-n}(x)$?

Published on 27 Mar 2026 - 4:38

score 230 · Answer 8 · 2020-07-17 08:06:02

230

Views

Integrate $\operatorname{PV}\int_0^{\infty}\frac{x\tan(\pi x)}{(1+x^2)^2}dx$

Published on 17 Jul 2020 - 8:06

score 33 · Answer 9 · 2020-07-17 12:55:17

33

Views

Equivalent of spectral density function related to fBm: $\sum_{k\in\mathbb{Z}}\vert \lambda+2k\pi\vert^{-2H-1}$

Published on 17 Jul 2020 - 12:55

score 53 · Answer 10 · 2026-03-25 07:42:06

53

Views

Evaluating $\int_0^{\infty} x^r \exp(e^{-s x}) e^{-ax^b}dx$

Published on 25 Mar 2026 - 7:42

score 364 · Answer 11 · 2026-03-31 15:45:48

364

Views

General integral $\int_0^{\frac{\pi}{p}}\ln\tan x \,dx $

Published on 31 Mar 2026 - 15:45

score 296 · Answer 12 · 2026-03-28 04:34:45

296

Views

About closed form or an upper bound on a summation of harmonic number

Published on 28 Mar 2026 - 4:34

score 107 · Answer 13 · 2026-03-25 22:05:43

107

Views

Find the constant for $\int_{0}^{1} {\frac{\mathrm{d}x}{\sqrt{(1-x^2)(1-(kx)^4)}}} \sim C\ln(1-k)$

Published on 25 Mar 2026 - 22:05

score 1.6k · Answer 14 · 2026-03-25 17:36:05

1.6k

Views

Bessel functions in terms of the confluent hypergeometric function

Published on 25 Mar 2026 - 17:36

score 39 · Answer 15 · 2020-07-23 04:26:59

Why does $\frac{n!n^x}{(x+1)_n}=\left(\frac{n}{n+1}\right)^x\prod_{j=1}^{n}\left(1+\frac{x}{j}\right)^{-1}\left(1+\frac{1}{j}\right)^x$

List Question

Beautiful closed form of $\sum_{k=0}^{\infty}\frac{(-1)^{k+1}}{2(k+1)^2}\int_0^1\ln (k+1-k^x)+2\ln (1+k^x)dx$

On Logarithmic Derivative transformation

On the series $\sum_{n=-\infty}^{\infty} \frac{\cos nx}{\Gamma\left ( a+n+1 \right ) \Gamma \left ( a-n+1 \right )}$

value of lommel function for negative first parameter and positive second parameter

Equality of the Schläfli's integrals

representation through special numbers

Closed-form expressions for the zeros of $\text{Li}_{-n}(x)$?

Integrate $\operatorname{PV}\int_0^{\infty}\frac{x\tan(\pi x)}{(1+x^2)^2}dx$

Equivalent of spectral density function related to fBm: $\sum_{k\in\mathbb{Z}}\vert \lambda+2k\pi\vert^{-2H-1}$

Evaluating $\int_0^{\infty} x^r \exp(e^{-s x}) e^{-ax^b}dx$

General integral $\int_0^{\frac{\pi}{p}}\ln\tan x \,dx $

About closed form or an upper bound on a summation of harmonic number

Find the constant for $\int_{0}^{1} {\frac{\mathrm{d}x}{\sqrt{(1-x^2)(1-(kx)^4)}}} \sim C\ln(1-k)$

Bessel functions in terms of the confluent hypergeometric function

Why does $\frac{n!n^x}{(x+1)_n}=\left(\frac{n}{n+1}\right)^x\prod_{j=1}^{n}\left(1+\frac{x}{j}\right)^{-1}\left(1+\frac{1}{j}\right)^x$

Trending Questions

Popular # Hahtags

Popular Questions