List questions from catalans-constant

Published on 01 May 2026 - 6:39

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

Published on 01 May 2026 - 6:39

309

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

Published on 01 May 2026 - 6:39

306

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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 06 May 2026 - 15:22

443

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

Published on 01 May 2026 - 6:39

245

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Riemann Zeta function and Catalan's constant

Published on 01 May 2026 - 6:39

419

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

Published on 01 May 2026 - 6:39

207

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A double sum identity for Catalan constant

Published on 01 May 2026 - 4:26

347

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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 01 May 2026 - 6:39

501

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

Published on 01 May 2026 - 4:25

275

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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 01 May 2026 - 6:39

128

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

Published on 01 May 2026 - 6:39

164

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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 Mar 2026 - 2:34

198

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Evaluation of tricky Gamma infinite sum

Published on 01 May 2026 - 6:39

106

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

Published on 01 May 2026 - 6:39

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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