Question

Another integral representation of Catalan's Constant?

score 751 · Answer 1 · 2023-07-06 23:44:48

751

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Another integral representation of Catalan's Constant?

Published on 06 Jul 2023 - 23:44

score 240 · Answer 2 · 2023-08-07 19:20:49

240

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Struggling to figure out why $\int\limits_{0}^{1}\frac{\ln \left(x^{2}\right)}{\left(1+x^{2}\right)^{2}}dx = -G-\frac{\pi}{4}$.

Published on 07 Aug 2023 - 19:20

score 795 · Answer 3 · 2023-09-04 19:25:43

795

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Is there an expression for $I(n)=\int_{0}^{\frac{\pi}{4}}x\tan^{n}x dx$?

Published on 04 Sep 2023 - 19:25

score 236 · Answer 4 · 2023-10-01 07:56:08

236

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Solve the integral $\int_0^1 \frac{\ln^2(x+1)-\ln\left(\frac{2x}{x^2+1}\right)\ln x+\ln^2\left(\frac{x}{x+1}\right)}{x^2+1} dx$

Published on 01 Oct 2023 - 7:56

score 263 · Answer 5 · 2023-10-03 19:31:54

263

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$I = \int_0^{\pi/2} \left( \int_0^{\pi/2} \frac{\log(\cos(x/2)) - \log(\cos(y/2))}{\cos(x) - \cos(y)} dx\right) \ dy $

Published on 03 Oct 2023 - 19:31

score 131 · Answer 6 · 2023-10-11 13:23:32

131

Views

closed form for $\psi^{(-2)}\left(\frac{1}{4} \right)$

Published on 11 Oct 2023 - 13:23

score 93 · Answer 7 · 2024-02-15 08:12:52

93

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$\int_0^1E(k)dk$ without switching integrals

Published on 15 Feb 2024 - 8:12

score 180 · Answer 8 · 2024-03-18 11:42:48

180

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Show that $\int_0^{\frac\pi 2}\frac{\theta-\cos\theta\sin\theta}{2\sin^3\theta}d\theta=\frac{2C+1}4$

Published on 18 Mar 2024 - 11:42

score 213 · Answer 9 · 2015-01-21 11:15:55

213

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How to find $ \sum_{k=0}^\infty \frac{(-1)^k}{(2k+1)^2}$?

Published on 21 Jan 2015 - 11:15

score 143 · Answer 10 · 2015-02-26 18:30:09

143

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Sum $\sum _{k=0}^{\infty } \frac{(-1)^k \psi (k+1)}{\left(k-\frac{3}{2}\right)^2}$

Published on 26 Feb 2015 - 18:30

score 124 · Answer 11 · 2015-11-20 01:56:39

124

Views

How to calculate this infinite sum?

Published on 20 Nov 2015 - 1:56

score 302 · Answer 12 · 2015-12-29 20:44:01

302

Views

Sum of infinite series - Catalan constant

Published on 29 Dec 2015 - 20:44

score 929 · Answer 13 · 2016-01-11 18:13:10

929

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Formulae for Catalan's constant.

Published on 11 Jan 2016 - 18:13

score 1.1k · Answer 14 · 2016-02-24 10:19:21

1.1k

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How to evaluate this integral $\int_{0}^{\infty }\frac{\ln\left ( 1+x^{3} \right )}{1+x^{2}}\mathrm{d}x$

Published on 24 Feb 2016 - 10:19

score 462 · Answer 15 · 2016-03-11 03:10:48

462

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How to evaluate $\int_{0}^{1}\frac{\arctan x}{1+x^{2}}\ln\left ( \frac{1+x^{2}}{1+x} \right )\mathrm{d}x$

Published on 11 Mar 2016 - 3:10

List Question

Another integral representation of Catalan's Constant?

Struggling to figure out why $\int\limits_{0}^{1}\frac{\ln \left(x^{2}\right)}{\left(1+x^{2}\right)^{2}}dx = -G-\frac{\pi}{4}$.

Is there an expression for $I(n)=\int_{0}^{\frac{\pi}{4}}x\tan^{n}x dx$?

Solve the integral $\int_0^1 \frac{\ln^2(x+1)-\ln\left(\frac{2x}{x^2+1}\right)\ln x+\ln^2\left(\frac{x}{x+1}\right)}{x^2+1} dx$

$I = \int_0^{\pi/2} \left( \int_0^{\pi/2} \frac{\log(\cos(x/2)) - \log(\cos(y/2))}{\cos(x) - \cos(y)} dx\right) \ dy $

closed form for $\psi^{(-2)}\left(\frac{1}{4} \right)$

$\int_0^1E(k)dk$ without switching integrals

Show that $\int_0^{\frac\pi 2}\frac{\theta-\cos\theta\sin\theta}{2\sin^3\theta}d\theta=\frac{2C+1}4$

How to find $ \sum_{k=0}^\infty \frac{(-1)^k}{(2k+1)^2}$?

Sum $\sum _{k=0}^{\infty } \frac{(-1)^k \psi (k+1)}{\left(k-\frac{3}{2}\right)^2}$

How to calculate this infinite sum?

Sum of infinite series - Catalan constant

Formulae for Catalan's constant.

How to evaluate this integral $\int_{0}^{\infty }\frac{\ln\left ( 1+x^{3} \right )}{1+x^{2}}\mathrm{d}x$

How to evaluate $\int_{0}^{1}\frac{\arctan x}{1+x^{2}}\ln\left ( \frac{1+x^{2}}{1+x} \right )\mathrm{d}x$

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