List questions from catalans-constant

Published on 20 Mar 2026 - 0:43

585

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Trigamma identity $\psi_1\left(\frac{11}{12}\right)-\psi_1\left(\frac{5}{12}\right)=4\sqrt 3 \pi^2-80G$

Published on 19 Mar 2026 - 14:31

293

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Series $\sum_{n=1}^{\infty}(-1)^n\frac{n}{(2n-1)^2}$

Published on 20 Mar 2026 - 1:23

1.5k

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Alternating sum of reciprocals of odd squares

Published on 19 Mar 2026 - 12:57

2.1k

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Evaluate $\int_{-\pi/4}^{\pi/4}\frac{x}{\sin x}\mathrm{d}x$

Published on 19 Mar 2026 - 13:23

1.6k

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Relationship between Catalan's constant and $\pi$

Published on 19 Mar 2026 - 23:12

485

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Conjecture $\sum\limits_{n=0}^{\infty}{2n \choose n}^22^{-4n} \frac{n(6n-1)}{(2n-1)^2(2n+1)}=\frac{2C}{\pi} $

Published on 19 Mar 2026 - 17:26

1.7k

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Why is Catalan's constant $G$ important?

Published on 19 Mar 2026 - 21:30

444

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Compute this following integral without Fourier series : $\int_0^{\pi/4}x\ln(\tan x)dx$

Published on 19 Mar 2026 - 13:42

187

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How would I evaluate the following integral in terms of Catalan's constant $\int_{0}^{\infty} \frac{xe^x}{1+e^{2x}}$?

Published on 19 Mar 2026 - 16:15

520

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Applying the Beukers-like irrationality proof for $\zeta(2)$ and $\zeta(3)$ to Catalan's constant: where does it fail?

Published on 17 Mar 2026 - 20:08

393

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Proving that $\int_0^\infty \frac{\operatorname{erf}(1/x)\operatorname{erfc}(1/x)}{x}dx=\frac{2G}{\pi}$

Published on 19 Mar 2026 - 13:35

894

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Integral $I=\int_0^\infty \frac{\ln(1+x)\ln(1+x^{-2})}{x} dx$

Published on 19 Mar 2026 - 22:46

837

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How to find $\int_{0}^{\pi/2} \log ({1+\cos x}) dx$ using real-variable methods?

Published on 19 Mar 2026 - 16:48

280

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Calculate $\int_0^1\frac{\log^2x\log(1+x^2)}{1-x^2}dx$

Published on 19 Mar 2026 - 18:46

List Question

Catalan's constant

Trigamma identity $\psi_1\left(\frac{11}{12}\right)-\psi_1\left(\frac{5}{12}\right)=4\sqrt 3 \pi^2-80G$

Series $\sum_{n=1}^{\infty}(-1)^n\frac{n}{(2n-1)^2}$

Alternating sum of reciprocals of odd squares

Evaluate $\int_{-\pi/4}^{\pi/4}\frac{x}{\sin x}\mathrm{d}x$

Relationship between Catalan's constant and $\pi$

Conjecture $\sum\limits_{n=0}^{\infty}{2n \choose n}^22^{-4n} \frac{n(6n-1)}{(2n-1)^2(2n+1)}=\frac{2C}{\pi} $

Why is Catalan's constant $G$ important?

Compute this following integral without Fourier series : $\int_0^{\pi/4}x\ln(\tan x)dx$

How would I evaluate the following integral in terms of Catalan's constant $\int_{0}^{\infty} \frac{xe^x}{1+e^{2x}}$?

Applying the Beukers-like irrationality proof for $\zeta(2)$ and $\zeta(3)$ to Catalan's constant: where does it fail?

Proving that $\int_0^\infty \frac{\operatorname{erf}(1/x)\operatorname{erfc}(1/x)}{x}dx=\frac{2G}{\pi}$

Integral $I=\int_0^\infty \frac{\ln(1+x)\ln(1+x^{-2})}{x} dx$

How to find $\int_{0}^{\pi/2} \log ({1+\cos x}) dx$ using real-variable methods?

Calculate $\int_0^1\frac{\log^2x\log(1+x^2)}{1-x^2}dx$

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