List questions from catalans-constant

Published on 29 Oct 2014 - 8:11

197

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A limit evaluating to $2 K$ (Catalan's constant)

Published on 29 Oct 2014 - 18:07

305

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$ \int_0^\infty dx\, x^{-3/4} \ln(1+x) \operatorname{Li}_2 \left( -\frac 1 x \right)$

Published on 19 Nov 2014 - 16:18

300

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$\int_0^{\pi/2} \sec^a(t)\,dt= \frac{\sqrt{\pi}}{2\Gamma\left(1-\frac{a}{2}\right)}\Gamma\left(\dfrac{1-a}{2}\right)$

Published on 23 Mar 2026 - 11:13

440

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Integral $\int_{0}^{\frac{\pi}{4}}x\ln(\cos x)dx$

Published on 07 Mar 2020 - 17:41

241

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Riemann Zeta function and Catalan's constant

Published on 07 May 2020 - 20:55

416

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How far have we got towards proving Catalan's constant is irrational?

Published on 08 Jun 2020 - 21:21

203

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A double sum identity for Catalan constant

Published on 29 Jun 2020 - 7:53

344

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How do I prove that $\int_0^1 \int_0^1 {{2+x^2-y^2}\over {2-x^2-y^2}} \, dx \, dy=2G?$

Published on 10 Jul 2016 - 15:58

499

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$\prod_{p=3 mod 4}{\frac{p^2-1}{p^2+1}}$, $p$ is prime.

Published on 22 Mar 2017 - 23:35

271

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For $n\ge m\ge 1$, how far can we walk with $ \int_0^{\frac{\pi}{2}} \frac{x^n}{\sin^m x} d x$?

Published on 29 Mar 2023 - 2:55

125

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Calculating a limit of a sequence of integrals that approaches the catalan constant

Published on 01 Apr 2023 - 13:51

163

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Is there a simple way to evaluate $\int_0^1 \arctan x \ln \left(\frac{1-x}{1+x}\right) d x?$

Published on 25 Apr 2023 - 10:17

194

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Evaluation of tricky Gamma infinite sum

Published on 20 May 2023 - 21:15

103

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Ways to solve $\int_0^{\frac{\pi}{2}} \frac{x}{\sin{x}}dx$

Published on 22 May 2023 - 16:52

List Question

Prove the integral evaluates to $\frac{K}{\pi}$

A limit evaluating to $2 K$ (Catalan's constant)

$ \int_0^\infty dx\, x^{-3/4} \ln(1+x) \operatorname{Li}_2 \left( -\frac 1 x \right)$

$\int_0^{\pi/2} \sec^a(t)\,dt= \frac{\sqrt{\pi}}{2\Gamma\left(1-\frac{a}{2}\right)}\Gamma\left(\dfrac{1-a}{2}\right)$

Integral $\int_{0}^{\frac{\pi}{4}}x\ln(\cos x)dx$

Riemann Zeta function and Catalan's constant

How far have we got towards proving Catalan's constant is irrational?

A double sum identity for Catalan constant

How do I prove that $\int_0^1 \int_0^1 {{2+x^2-y^2}\over {2-x^2-y^2}} \, dx \, dy=2G?$

$\prod_{p=3 mod 4}{\frac{p^2-1}{p^2+1}}$, $p$ is prime.

For $n\ge m\ge 1$, how far can we walk with $ \int_0^{\frac{\pi}{2}} \frac{x^n}{\sin^m x} d x$?

Calculating a limit of a sequence of integrals that approaches the catalan constant

Is there a simple way to evaluate $\int_0^1 \arctan x \ln \left(\frac{1-x}{1+x}\right) d x?$

Evaluation of tricky Gamma infinite sum

Ways to solve $\int_0^{\frac{\pi}{2}} \frac{x}{\sin{x}}dx$

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