Question

Integral related to $\frac{\sqrt{2}K(\sqrt{\frac{2k}{1+k}})}{\sqrt{1+k}}$.

score 372 · Answer 1 · 2026-03-26 12:37:56

372

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Integral related to $\frac{\sqrt{2}K(\sqrt{\frac{2k}{1+k}})}{\sqrt{1+k}}$.

Published on 26 Mar 2026 - 12:37

score 61 · Answer 2 · 2026-03-26 04:29:33

61

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Asymptotic behavior of Regularized Gamma Function

Published on 26 Mar 2026 - 4:29

score 184 · Answer 3 · 2023-12-17 05:38:58

184

Views

Curious improper integral:$\displaystyle\int_0^\infty\dfrac{\sin(x^3)}{x^2}dx$

Published on 17 Dec 2023 - 5:38

score 117 · Answer 4 · 2026-03-25 15:57:07

117

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Function with sum equals function which uses digamma function

Published on 25 Mar 2026 - 15:57

score 77 · Answer 5 · 2026-03-26 04:36:36

77

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$X$ has gamma distribution with parameters $\alpha = \frac{1}{3}, \ \beta = n.$ Find $\lim_{n \longrightarrow \infty} P(|X_n-3n|<x\sqrt{n})$

Published on 26 Mar 2026 - 4:36

score 70 · Answer 6 · 2026-03-26 04:36:44

70

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Modeling the probability of observing $N$ photons in an interval of time

Published on 26 Mar 2026 - 4:36

score 48 · Answer 7 · 2026-03-25 17:28:25

48

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Estimating derivative involving the gamma function

Published on 25 Mar 2026 - 17:28

score 52 · Answer 8 · 2023-12-26 08:06:16

52

Views

Show that $\int^1_0 \mathrm{d}x \frac{x^2}{\sqrt{1-x^4}} = \frac{\sqrt{\pi}}{3}\frac{\Gamma(7/4)}{\Gamma(5/4)}$

Published on 26 Dec 2023 - 8:06

score 142 · Answer 9 · 2023-12-29 00:54:21

142

Views

Good definition of the Gamma function

Published on 29 Dec 2023 - 0:54

score 62 · Answer 10 · 2026-03-26 12:58:15

62

Views

How is the Gamma function related to the Golden Ratio?

Published on 26 Mar 2026 - 12:58

score 337 · Answer 11 · 2026-03-26 04:35:00

337

Views

Insurance company with claims following a Poisson Process. Calculate the probability that the capital is always positive throughout the first 4 days.

Published on 26 Mar 2026 - 4:35

score 86 · Answer 12 · 2026-03-27 07:48:16

86

Views

How to prove the relation between Beta and Gamma functions?

Published on 27 Mar 2026 - 7:48

score 90 · Answer 13 · 2026-03-30 05:30:14

90

Views

Find limit: $\lim_{s\to n}\frac{\Gamma'(1-s)}{\Gamma^2(1-s)}$

Published on 30 Mar 2026 - 5:30

score 332 · Answer 14 · 2026-03-29 05:35:02

332

Views

(1/2)! from the infinite product definition of gamma

Published on 29 Mar 2026 - 5:35

score 31 · Answer 15 · 2024-01-06 16:59:35

31

Views

Showing the asymptotic behavior of the expectation of a function of a Galton-Watson process using the Stirling formula

Published on 06 Jan 2024 - 16:59

List Question

Integral related to $\frac{\sqrt{2}K(\sqrt{\frac{2k}{1+k}})}{\sqrt{1+k}}$.

Asymptotic behavior of Regularized Gamma Function

Curious improper integral:$\displaystyle\int_0^\infty\dfrac{\sin(x^3)}{x^2}dx$

Function with sum equals function which uses digamma function

$X$ has gamma distribution with parameters $\alpha = \frac{1}{3}, \ \beta = n.$ Find $\lim_{n \longrightarrow \infty} P(|X_n-3n|<x\sqrt{n})$

Modeling the probability of observing $N$ photons in an interval of time

Estimating derivative involving the gamma function

Show that $\int^1_0 \mathrm{d}x \frac{x^2}{\sqrt{1-x^4}} = \frac{\sqrt{\pi}}{3}\frac{\Gamma(7/4)}{\Gamma(5/4)}$

Good definition of the Gamma function

How is the Gamma function related to the Golden Ratio?

Insurance company with claims following a Poisson Process. Calculate the probability that the capital is always positive throughout the first 4 days.

How to prove the relation between Beta and Gamma functions?

Find limit: $\lim_{s\to n}\frac{\Gamma'(1-s)}{\Gamma^2(1-s)}$

(1/2)! from the infinite product definition of gamma

Showing the asymptotic behavior of the expectation of a function of a Galton-Watson process using the Stirling formula

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