Question

Maximum of independent beta random variables.

score 733 · Answer 1 · 2017-03-31 21:53:35

733

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Maximum of independent beta random variables.

Published on 31 Mar 2017 - 21:53

score 104 · Answer 2 · 2017-04-04 10:10:25

104

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Need help calculating a definite integral

Published on 04 Apr 2017 - 10:10

score 105 · Answer 3 · 2023-02-06 18:24:23

105

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Let $ f(x) = x^{ \alpha-1}(1+x)^{- \alpha-\beta}\frac{Γ(α+β)}{Γ(α)Γ(β)},$ where $Γ(x) = (x − 1)Γ(x-1)$ and $α,β > 1$.

Published on 06 Feb 2023 - 18:24

score 104 · Answer 4 · 2023-02-10 21:24:45

104

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Limit of the Incomplete Beta Function special case

Published on 10 Feb 2023 - 21:24

score 151 · Answer 5 · 2026-03-20 02:21:58

151

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Double series with Beta reciprocals $\sum_{j=0}^\infty \sum_{k=0}^\infty \frac{x^j}{j!}\frac{y^k}{k!} \frac{1}{\boldsymbol{B}(j+1,k+1)} = ? $

Published on 20 Mar 2026 - 2:21

score 62 · Answer 6 · 2023-02-11 13:40:35

62

Views

Closed form for $B(1-z\omega,1-z\omega^2)$ where $B(z_1,z_2)$ is the Beta function and $\omega$ is a cube root of unity

Published on 11 Feb 2023 - 13:40

score 114 · Answer 7 · 2023-02-11 14:03:24

114

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Unable to understand usage of the Beta function in a previous question

Published on 11 Feb 2023 - 14:03

score 165 · Answer 8 · 2023-02-15 14:05:32

165

Views

To evaluate integral using Beta function

Published on 15 Feb 2023 - 14:05

score 51 · Answer 9 · 2023-02-19 16:03:47

51

Views

Closed formula for $\int_{0}^{1} (1-x)^{n-a} \cdot x^{a} \cdot \exp\left(i\alpha x\right) \ dx$

Published on 19 Feb 2023 - 16:03

score 116 · Answer 10 · 2023-02-27 08:37:08

116

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Investigate on the convergence of $I(a)= \int_0^{\infty} \frac{x}{\sqrt{1+x^a}} d x $ for $a>0$ and its exact value in case of convergence.

Published on 27 Feb 2023 - 8:37

score 52 · Answer 11 · 2023-03-06 13:59:13

52

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How to prove $\frac{\mathcal{B}(\frac{1}{2},\frac{1}{6})}{3} = -\mathcal{B}(-\frac{1}{2},\frac{7}{6})$

Published on 06 Mar 2023 - 13:59

score 148 · Answer 12 · 2026-03-25 15:41:22

148

Views

How to solve $\int_{-1}^{\infty}\frac{dx}{\sqrt{x^3+1}}$

Published on 25 Mar 2026 - 15:41

score 126 · Answer 13 · 2026-03-26 06:27:45

126

Views

How to cancel this Jacobi amplitude, elliptic integral, and incomplete beta function composition?

Published on 26 Mar 2026 - 6:27

score 336 · Answer 14 · 2023-03-14 08:07:26

336

Views

Can we evaluate the integral using Feynman’s, Frullani’s or double integral without Beta functions?

Published on 14 Mar 2023 - 8:07

score 42 · Answer 15 · 2023-03-18 14:33:36

42

Views

Area calculation of Burnside Curve

Published on 18 Mar 2023 - 14:33

List Question

Maximum of independent beta random variables.

Need help calculating a definite integral

Let $ f(x) = x^{ \alpha-1}(1+x)^{- \alpha-\beta}\frac{Γ(α+β)}{Γ(α)Γ(β)},$ where $Γ(x) = (x − 1)Γ(x-1)$ and $α,β > 1$.

Limit of the Incomplete Beta Function special case

Double series with Beta reciprocals $\sum_{j=0}^\infty \sum_{k=0}^\infty \frac{x^j}{j!}\frac{y^k}{k!} \frac{1}{\boldsymbol{B}(j+1,k+1)} = ? $

Closed form for $B(1-z\omega,1-z\omega^2)$ where $B(z_1,z_2)$ is the Beta function and $\omega$ is a cube root of unity

Unable to understand usage of the Beta function in a previous question

To evaluate integral using Beta function

Closed formula for $\int_{0}^{1} (1-x)^{n-a} \cdot x^{a} \cdot \exp\left(i\alpha x\right) \ dx$

Investigate on the convergence of $I(a)= \int_0^{\infty} \frac{x}{\sqrt{1+x^a}} d x $ for $a>0$ and its exact value in case of convergence.

How to prove $\frac{\mathcal{B}(\frac{1}{2},\frac{1}{6})}{3} = -\mathcal{B}(-\frac{1}{2},\frac{7}{6})$

How to solve $\int_{-1}^{\infty}\frac{dx}{\sqrt{x^3+1}}$

How to cancel this Jacobi amplitude, elliptic integral, and incomplete beta function composition?

Can we evaluate the integral using Feynman’s, Frullani’s or double integral without Beta functions?

Area calculation of Burnside Curve

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