Question

About the integral $\int_{0}^{\pi/4}\log^4(\cos\theta)\,d\theta$

score 728 · Answer 1 · 2026-03-26 16:06:12

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About the integral $\int_{0}^{\pi/4}\log^4(\cos\theta)\,d\theta$

Published on 26 Mar 2026 - 16:06

score 58 · Answer 2 · 2026-03-25 06:31:41

58

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Dirac Delta special case

Published on 25 Mar 2026 - 6:31

score 519 · Answer 3 · 2026-03-25 12:31:09

519

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On the integral $\int_{0}^{1/2}\frac{\text{Li}_3(1-z)}{\sqrt{z(1-z)}}\,dz$

Published on 25 Mar 2026 - 12:31

score 232 · Answer 4 · 2026-03-25 05:57:41

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Sufficient statistics for beta-binomial distribution

Published on 25 Mar 2026 - 5:57

score 179 · Answer 5 · 2026-03-25 18:52:08

179

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Use the $\Gamma$ function to solve $\int_{-\infty}^{\infty} e^{xt - e^{t}} dt$

Published on 25 Mar 2026 - 18:52

score 585 · Answer 6 · 2026-03-19 14:31:15

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

score 46 · Answer 7 · 2018-05-31 14:22:39

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Can $‎f(x)=\ln \left\{‎\prod‎_{n=1}^{‎\infty‎}\left(\frac{1}{‎(-a^{n+1};a)_x}\right){‎(-a;a)_{‎\infty‎}}^x\right\}‎$ be simpler?

Published on 31 May 2018 - 14:22

score 1k · Answer 8 · 2026-03-25 18:50:16

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Simplify $\Gamma\left(\frac27\right) \Gamma\left(\frac{11}{42}\right)/\;\Gamma\left(\frac1{21}\right)$ to elementary terms

Published on 25 Mar 2026 - 18:50

score 182 · Answer 9 · 2026-03-25 01:15:11

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Simplifying an infinite fraction

Published on 25 Mar 2026 - 1:15

score 27 · Answer 10 · 2018-06-02 11:58:19

27

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Find the limit of $‎\mu_n(x)=‎x\psi(n+1)‎+\sum_{k=1}^n‎\left(‎\psi(k+1)-‎\psi(k+1+x)\right)$?

Published on 02 Jun 2018 - 11:58

score 623 · Answer 11 · 2026-03-25 05:50:17

623

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Showing that $\Gamma(x)\Gamma(y) = \Gamma(x+y)\beta(x,y)$ via change of variable

Published on 25 Mar 2026 - 5:50

score 406 · Answer 12 · 2026-03-25 09:50:07

406

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$ y = \int_1^{\infty} \frac{\operatorname{li}(x)^2 (x - 1)}{x^4} dx $

Published on 25 Mar 2026 - 9:50

score 104 · Answer 13 · 2018-06-08 16:35:21

104

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Incomplete multivariate Gamma function

Published on 08 Jun 2018 - 16:35

score 125 · Answer 14 · 2026-03-25 22:30:11

125

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Indefinite integral whose solution involves W Lambert, $\int e^{bcos(ct)-at} dt $

Published on 25 Mar 2026 - 22:30

score 37 · Answer 15 · 2026-03-25 10:57:25

37

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A Particular Function from the Set of Unordered Pairs of Rational Numbers to the Rationals

Published on 25 Mar 2026 - 10:57

List Question

About the integral $\int_{0}^{\pi/4}\log^4(\cos\theta)\,d\theta$

Dirac Delta special case

On the integral $\int_{0}^{1/2}\frac{\text{Li}_3(1-z)}{\sqrt{z(1-z)}}\,dz$

Sufficient statistics for beta-binomial distribution

Use the $\Gamma$ function to solve $\int_{-\infty}^{\infty} e^{xt - e^{t}} dt$

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

Can $‎f(x)=\ln \left\{‎\prod‎_{n=1}^{‎\infty‎}\left(\frac{1}{‎(-a^{n+1};a)_x}\right){‎(-a;a)_{‎\infty‎}}^x\right\}‎$ be simpler?

Simplify $\Gamma\left(\frac27\right) \Gamma\left(\frac{11}{42}\right)/\;\Gamma\left(\frac1{21}\right)$ to elementary terms

Simplifying an infinite fraction

Find the limit of $‎\mu_n(x)=‎x\psi(n+1)‎+\sum_{k=1}^n‎\left(‎\psi(k+1)-‎\psi(k+1+x)\right)$?

Showing that $\Gamma(x)\Gamma(y) = \Gamma(x+y)\beta(x,y)$ via change of variable

$ y = \int_1^{\infty} \frac{\operatorname{li}(x)^2 (x - 1)}{x^4} dx $

Incomplete multivariate Gamma function

Indefinite integral whose solution involves W Lambert, $\int e^{bcos(ct)-at} dt $

A Particular Function from the Set of Unordered Pairs of Rational Numbers to the Rationals

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